• 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