It depends on the cheese. With a hard cheese, yes. With a soft one, no.
Hard, dense cheeses like cheddar, Parmigiano Reggiano and Gruyère don't give mold much room to travel, so a small spot on the surface can be cut away. Cut at least 1 inch (about 2.5 cm) around and below the moldy spot, and keep the tip of your knife out of the mold so you don't drag it across clean cheese. Then wrap what's left in fresh paper or wrap. This lines up with the USDA's general advice on mold and cheese.
Throw it out instead if the cheese is:
- Soft or fresh (ricotta, cream cheese, cottage cheese, fresh mozzarella, fresh chèvre). Moisture lets mold threads, and any bacteria that came along with them, spread well beyond what you can see.
- Shredded, crumbled or sliced. Mold spreads easily through the pieces and is hard to spot.
- Slimy, or smells off in a way that has nothing to do with that cheese's normal funk.
Cheeses that are made with mold on purpose, like Brie, Camembert and blue cheeses, are a different story. That mold is supposed to be there. But if a different mold (fuzzy green, black or pink) shows up on a soft cheese, toss it.
And the usual rule applies: if you're not sure, it isn't worth the stomachache.
Related: How should I store leftover cheese? · Can cheese be frozen? · Should cheese be kept in the fridge? · How can you tell if cheese has gone bad? · How long does cheese last? · What are the crunchy white crystals in aged cheese?