This phase III trial studies how well pressurized intraperitoneal aerosolized chemotherapy (PIPAC) with mitomycin works versus (vs) standard chemotherapy (leucovorin calcium, fluorouracil, and irinotecan hydrochloride \[FOLFIRI regimen\] plus bevacizumab) in treating patients with appendix or colorectal cancer that cannot be removed by surgery (unresectable) and has spread from where it first started (primary site) to the abdominal cavity (peritoneal metastases). PIPAC is a new therapeutic approach that is minimally invasive, does not require surgery (laparotomy), and can be frequently repeated. Chemotherapy is delivered as a pressurized mist directly inside the abdominal cavity (peritoneum) during a minimally invasive surgery called a laparoscopy. The pressure helps the chemotherapy absorb into the cancer tissue and spread more evenly. Mitomycin is an antibiotic used as a chemotherapy drug. It stops or slows the growth of cancer cells and other rapidly growing cells by damaging their deoxyribonucleic acid (DNA). Standard chemotherapy drugs, such as those in the FOLFIRI regimen, are given via infusion into a vein (intravenously), and work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Another standard intravenous drug, bevacizumab, is in a class of medications called antiangiogenic agents. It works by stopping the formation of blood vessels that bring oxygen and nutrients to tumor. This may slow the growth and spread of tumor. Giving mitomycin via PIPAC in combination with the standard FOLFIRI regimen, with or without bevacizumab, may work better than standard FOLFIRI plus bevacizumab alone in treating patients with unresectable appendix or colorectal cancer with peritoneal metastases.