I found the problem -- the event that says "Card - Spawn card etc. etc.". If you set text to display the number of cards, you'll see it's actually spawning in powers of two; 2, 4, 8, 16, 32, 64, until it reaches THOUSANDS of cards spawned in the same spot every time you click. Hence the slowdown.
You can fix it by switching out that line for "System - Create Card at Mouse.X, Mouse.Y". Accomplishes the same thing without that messy situation!