The 1st thing you need to do is make sure you do not have any exhaust leaks and you have spark plugs in good condition.
Next...
Make sure you tank is venting. It will run with positive pressure or 0 pressure, but it will not run in vacuum. Verify there is no water in the fuel tank. Make sure all of your fuel lines are in good condition and have a good seal around the nipple as to not suck air. Ensure your fuel petcock (if you have one) and fuel filter is clean and clear with no blockage of flow. Try riding it again...
Next...
If still problems, buy a pop-off gauge and remove your carbs. Check your pop-off before you do anything else with you carbs so you know if it was right or wrong to start. Remove all parts on the diaphragm side and clean them. Replace needle and seat if leaking (as would be seen from pop-off test) and recheck pop-off with new needle and seat. Remove adjustment screws and clean (You probably have access to your screws but if not, remove the plugs so you can access the screws). Open fuel pump side and clean thoroughly, make sure all sealing surfaces are clean, o-rings are in good repair. Remove internal fuel filter (fuel pump side) and clean or replace it. If you have any doubts about your fuel pump condition, or if you have leaking pop-off after replacing the needle and seat, then rebuild the carb using genuine mikuni rebuild kits (SBT rebuild kits are junk). Make sure you reinstall everything correctly, there are a lot of parts in there. Recheck pop-off, it must be right by this point or you must find the cause. Everything at this point should be clean and debris free, with properly moving needle screw adjusters, idle screw adjusters and chock/throttle plates.
Reassemble the ski. Tell us how it runs.