Automatic Clamping advice

They do sell solenoid pinch valves specifically for that purpose. I've noticed they're quite expensive, probably because of their typical medical or scientific application (other applications will usually just use a standard solenoid valve). You might be able to get a deal on surplus pinch valves if you get lucky on eBay. I think you may be limited to certain properties of tubing.

Possibly more fun/cheap would be to find a DIY solution. Solenoids are fairly cheap, you just need to get one with enough force and build the pinch parts. Even if you don't need a pump, the mechanisms you find in DIY peristaltic pumps could be adapted to work as a pinch valve if for some reason you found using a motor preferable to a solenoid.