While it is possible to cut MDF by repeatedly scoring it with a knife, it's a terrible way of going about it.
Better by far to just bite the bullet and get yourself a gents saw. You can spend as much as you like on these, but I've had years of good service from one that only cost me about 15 dollars (kiwibucks).
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I also cobbled together a simple mitre box for my little modeller's razor saw out of scraps of 18mm MDF that makes cutting 90 and 45 degree angles a breeze. It's not necessary, but it will certainly make life easier.