I have bought strips of rubber, that are cut from a sheet. They used a tool with a spinning disc that had well polished sides and a knife edge. Think of a spinning pizza cutter.
Brady's drag knife approach makes sense. Spraying with a lubricant would help.
Freezing it would allow a rotary cutter to work. And, thinking of someone other than myself running from large freezer to bot with a large, brittle sheet of rubber; well, that would make me feel better about some of my antics over the years.
But, if you're tempted to freeze, here's my 2 cents worth: get a metal channel to lay over the cut. fill it with dry ice, move it over to next location, while cutting the first.