If it has a excelerator pump it might be cloged. The excelerator pump has very small holes that are hard to clear if cloged. The pump will be round with 3 screws on the bottom of the carb next to the float bowl normally on the same side as the throttle linkage. If the pump is not cloged.
I would lift the needle(richen the needle circut) in the carb and try one size larger pilot jet you may need to adjust the mixture screw in a bit to get the idle back.
If your slide has a diafram on it it is a CV carb. CV carbs the slide is not directly connected to the throttle linkage it moves by engine vacume the throttle controls a butterfly between the slide and the engine. If it has one of these it needs to move smoothly and should pump air and have a vacume in both directions controled by a small hole near the top. Factorys jet kits sometimes adjust the size of this hole on sportbikes. Dynojet adjusts the spring.
Does it do it as you open the throttle or at steady throtlte.
Also this web site has lots of info.
http://www.jdjetting.com/