Ivonescimab Before Surgery for the Treatment of Resectable Stage II-IV Head and Neck Cancer

Inclusion Criteria: * At least 18 years of age * PD-L1 combined positive score (CPS) \>= 1 * Histologically documented advanced stage mucosal HNSCC (stage II-IV), for which surgery would be recommended in routine clinical practice * Primary tumor is amenable to fresh biopsy or availability of archival fresh frozen primary tissue * Eastern Cooperative Oncology Group (ECOG) 0-1 * Absolute neutrophil count \> 1500 cells/uL * Platelet count \>= 100,000/uL * Hemoglobin \>= 9.0 g/dL (without transfusion within 14 days prior to cycle 1, day 1) * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) or =\< 3 x ULN for participants with Gilbert's disease * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x institutional ULN * Creatinine =\< 1.5 x institutional ULN OR estimated glomerular filtration rate (eGFR) value \>= 30/mL using the Chronic Kidney Disease Epidemiology (CKD-EPI) equation OR measured (OR calculated) creatinine clearance \>= 50 mL/min using the Cockcroft-Gault Formula * Urine protein \< 2+ or 24-hour urine protein quantification \< 1.0 g * Prothrombin time (PT) or international normalized ratio (INR) =\< 1.5 x ULN, and partial thromboplastin time (PTT) or activated (a)PTT =\< 1.5 x ULN (unless abnormalities are unrelated to coagulopathy) This applies only to patients who are not on therapeutic anti-coagulation * For patients receiving therapeutic anti-coagulation there are no coagulation parameters for eligibility. However, patients should be on a stable dose * Female patients of childbearing age per institutional definition must have negative serum pregnancy test results before enrollment * Female patients of childbearing potential having sex with an unsterilized male partner must agree to use a highly effective method of contraception from the beginning of screening until 90 days after the last dose of ivonescimab * Unsterilized male patients having sex with a female partner of childbearing potential, or a pregnant or breastfeeding partner must agree to use barrier contraception (male condom) for the duration of the treatment period until 90 days after the last dose of ivonescimab. Male patients with female partners of childbearing potential must have the female partner agree to use at least 1 form of highly effective contraception for the duration of the treatment period until 90 days after the last dose of ivonescimab * Ability to understand and the willingness to sign a written informed consent * Deemed to be a candidate for trial therapy by University of Michigan providers in both Medical Oncology and Otolaryngology or Oral and Maxillofacial Surgery Exclusion Criteria: * Prior radiation therapy for treatment of the current mucosal HNSCC (patients undergoing salvage resection are excluded) * Prior neck dissection on the side of current mucosal HNSCC * Major surgical procedures or serious trauma within 4 weeks prior to enrollment. Minor local procedures (excluding central venous catheterization, port implantation, and tumor biopsy) within 3 days prior to planned cycle 1, day 1 * History of bleeding tendencies or coagulopathy and/or clinically significant bleeding symptoms or risk within 4 weeks prior to enrollment * Nasal bleeding / epistaxis (bloody nasal discharge is allowed) graded as \>= grade 2 by Common Terminology Criteria for Adverse Events (CTCAE) version (v)5.0 within 14 days prior to registration * Current use of prophylactic or full-dose anticoagulants or anti-platelet agents for therapeutic purposes that is not stable prior to enrollment is not allowed. The use of full-dose anticoagulants is permitted as long as INR or aPTT is within therapeutic limits * Patients with a condition requiring corticosteroid therapy (\> 10 mg prednisone/day or equivalent) within 14 days of the first dose of study drug. Exceptions: Physiologic replacement doses are allowed even if they are \> 10 mg of prednisone/day or equivalent, as long as they are not being administered for immunosuppressive intent. Inhaled or topical steroids are permitted, provided that they are not for treatment of an autoimmune disorder * Patients with active, known, or suspected autoimmune disease that has required systemic therapy within 5 years of the projected enrollment date. Exceptions: Patients with vitiligo, type I diabetes mellitus, and endocrinopathies (including hypothyroidism due to autoimmune thyroiditis) only requiring hormone replacement, childhood asthma that has resolved, or psoriasis that does not require systemic treatment are permitted * Patients with symptomatic central nervous system (CNS) metastases, CNS metastases with hemorrhagic features, CNS metastasis \>= 1.5 cm, CNS radiation within 7 days prior to randomization, potential need for CNS radiation within the first cycle, or leptomeningeal disease * Recipient of a solid organ or allogeneic stem cell transplant * Patients with active hepatitis B (Patients with stable or declining levels of hepatitis B deoxyribonucleic acid \[DNA\] by polymerase chain reaction \[PCR\] on appropriate anti-viral therapy with acceptable tolerability for one month prior to enrollment will not be excluded) * Patients with active hepatitis C (hepatitis C virus \[HCV\] antibody positive with HCV ribonucleic acid \[RNA\] levels above the lower limit of detection) * Known allergy or hypersensitivity to any component of the study drug or any excipients (histidine, histidine hydrochloride, sucrose, polysorbate 80 (II), and water for injection); known history of severe hypersensitivity to other monoclonal antibodies * Patient is breastfeeding or plans to breastfeed during study participation * Radiographic evidence of major blood vessel encasement with narrowing of the vessel that the investigator determines will pose a significantly increased risk of bleeding * Live vaccine or live attenuated vaccine received within 4 weeks prior to planned enrollment or scheduled to receive a live vaccine or live attenuated vaccine during the study period. Inactivated vaccines are permitted * History of non-infectious pneumonia requiring systemic corticosteroids, or current interstitial lung disease * Has pre-existing peripheral neuropathy that is \>= grade 2 by CTCAE version 5 * History of esophageal gastric varices, severe ulcers, wounds that do not heal, abdominal fistula, intra-abdominal abscesses, or acute gastrointestinal bleeding within 6 months before enrollment * Acute exacerbation of chronic obstructive pulmonary disease within 4 weeks before enrollment * History of perforation of the gastrointestinal tract and/or fistula, history of gastrointestinal obstruction (including incomplete intestinal obstruction requiring parenteral nutrition), extensive bowel resection (partial colectomy or extensive small bowel resection) within 6 months prior to enrollment * Known history of human immunodeficiency virus (HIV) whose viral load is not controlled * Participant has active cardiovascular disease including, but not limited to: * Thromboembolism * Medical history of any grade arterial thromboembolic event, grade 3 and above venous thromboembolic event (as specified in NCI CTCAE 5.0) * Cardiovascular disease * Any of the following within 12 months prior to enrollment: * Myocardial infarction * Unstable angina * Unstable vascular disease (eg, aortic aneurysm at risk of rupture, Moyamoya disease) * Transient ischemic attack * Cerebrovascular accident * Hypertensive Crisis * Hypertensive encephalopathy * Coronary stent placement * Clinically non-significant thrombosis, such as non-obstructive catheter-associated thrombus, incidental or asymptomatic pulmonary embolism, are not exclusionary * Hypertension * Uncontrolled (persistent) hypertension: * Systolic blood pressure \> 160 mmHg; diastolic blood pressure \> 100 mmHg * Heart failure * Congestive heart failure (CHF), defined as New York Heart Association (NYHA) class III-IV or hospitalization for CHF within 12 months prior * Participant has uncontrolled illness including, but not limited to: * Severe infection within 4 weeks prior to enrollment, including but not limited to comorbidities requiring hospitalization, sepsis, or severe pneumonia; active infection (as determined by the investigator) requiring systemic anti-infective therapy within 2 weeks prior to enrollment (excluding antiviral therapy for hepatitis B or C) * Uncontrolled diabetes * Ongoing or active infection (includes infection requiring treatment with antimicrobial therapy) * Psychiatric illness, social situation, or any other circumstances that would limit compliance with study requirements * Active bleeding diathesis requiring anticoagulant or antiplatelet therapy