Can you cut the mold off food and eat the rest?

The answer splits on texture. On hard, dense foods, hard cheeses like cheddar and parmesan, firm fruits and vegetables like carrots and cabbage, mold cannot spread its threadlike roots very far, so the USDA says to cut at least an inch around and below the moldy spot, keep the knife out of the mold itself, and the rest is fine. Salami and dry-cured hams with surface mold are also generally salvageable by scrubbing.

Soft and moist foods are the opposite: toss them entirely. Bread, soft cheeses, yogurt, jam, cooked leftovers, and soft fruits like berries and peaches let mold send invisible roots and, in some cases, toxins throughout, so the visible fuzz is only part of what is present, and cutting it off leaves the hidden portion behind. The green fuzz on one strawberry is a reason to inspect the whole box. A special note on bread: the mold you see has already spread through the loaf's soft crumb, so picking off the spot does not make the slice safe. Some molds produce mycotoxins, and while a nibble rarely causes serious harm, the safe rule is that soft moldy food is trash, hard moldy food can often be trimmed.