How to Cut a sponge in half for a project?

Foam is funny. If scissors don't work, try a serrated bread knife.

Smash it flat with a heavy book on each side, or have someone hold it like that. Then cut through with good fabric scissors. If you are using paper-cutting scissors, that is probably your problem. Also, an electric turkey carving knife will make short work of it.

How big is the 'sponge'? If it is a large piece of foam, an electric knife, as Bpi mentioned, cuts cleanly through foam.

Place sponge in water till it absorbs as much water as possible. Freeze it till rock hard. Cut it with your table saw or skill saw.

Place it on a hard surface you don't mind marking up. Cutting board would work. Lay a book, board, etc., along the cut line. Press down and cut with a razor knife, serrated knife, Chef's knife.

Some sponges can be torn easier than cutting them ... or ...carefully use an utility knife and just keep scoring the same line until you cut thru.