I see that Jake used a bread knife to cut his foam mattress.
But I'll tell you what REALLY works well to cut foam rubber: an electric carving knife -- the kind with two blades that run back and forth alongside each other. Commonly used for slicing meat, turkey etc. A few bucks wherever small kitchen appliances are sold.
I'd sure be leery of any used mattress. New foam is not all that expensive. I just paid... hmmm... something around $75 for a Queen, four inches thick. To cut it in halves, I laid a sheet of plywood on top of it, which allowed me to crawl on the plywood while I cut.