Sounds like a fuel problem. I would make sure you are getting plenty of fuel to the carburetor. If that is good I would completely disassemble the carburetor, remove the jets, main nozzle, air screw and give them a good soak in carb cleaner. Blow them out and look through them to make sure there isn't any crud left. Clean the slide and needle jet with cleaner and blow off with compressed air.
While you have the carburetor apart check the float valve (needle and seat) for any defects. Make sure there isn't a ridge in the needle. It's very rare but check the and make sure the float isn't cracked fuel getting into it. When you reassemble the float valve check the float height as well and adjust the air screw. Usually 1 1/2 to 2 turns out from seated is a good start.
Some other questions before moving on to other things.
Have you owned it for a while and it just started doing this?
Any aftermarket items - pipe, reeds, cylinder mods, etc?
What year is it?
That little quad has been around for many years and has a huge following. There are a few good Blaster forums out there that have a lot of good info posted. you can probably find out anything you want to know about the Blaster on those forums.
Suspect the TORS system.
Pasted from http://answers.yahoo.com/question/index?qid=20081114193501AAUw67m
Take the carb off, make sure your reeds are there and in good shape, none broken or bent. Replace the reeds if in doubt. Have you thought about the TORS system preventing your bike from reaching full throttle? The TORS is there to prevent runaways; if the handlebar throttle is in the idle position but the carb is in the full-throttle position, the bike will shut down. Locate the TORS harness on the carb and bypass it with a paper clip or a small section of wire. Now try giving the bike full throttle. If the bypass worked, then I suggest you remove it, it is there as a safety feature but most people and especially racers remove it. Also, check the carb slide to make sure that it does open fully, if not you will need to make the proper adjustments. I hope all of this helps, good luck.