Apparently a lot of modern linoleum used for homes has some kind of gritty additive in it that dulls tools quickly. But "battleship linoleum", normally coloured brown or gray, is a higher grade that cuts well - this is probably the stuff you pay so much for at art supply stores.

Any kind of linoleum will cut much better if you just heat it a little bit. Light bulb, warm oven, even strong sunlight will improve it.

Hanging around dumpsters will get you far! They just have to be the right dumpsters.