So which clutch are you refering to? The one connected to the engine or the one connected to the rear axle? In addtion what exactly is happening or not happening?
Here is a short video of how the clutches should run as the engine speeds up
In this case the engine (or drive) clutch is on the left which is the opposite of what you have but that doesn't matter. Put the cart on axle stands and get a friend to blip the throttle (don't torture the engine) and see if it looks like the video.
Report back and we can get you fixed up
Dave