This is not a strange problem. Fairly common.
1st, you should have a small amount of play in the cable, about a dime thickness.
2nd, turn the gas off and lay the bike down on the left(gear shifter)side.
3rd remove the clutch cover and inspect the basket. The oil will remain in the bike.
2 posibilities.
First is "notched" clutch basket fingers. This can be repaired if it is not too severe. Remove the preasure plate, fiber, and metal plates if these are very rough, you'll need to go ahead and drain the oil and lightly file the clutch fingers. The plates need to freely expand when the clutch is engaged, the notches fight or prevent the expansion of the clutch pack. Check all of the plate splines and tangs for sharp edges and file lightly. Clean everything thoroughly and reinstall. Fill with oil and ride. If the notches are extreme, the real cure is a new basket, preasure plate, and clutch plates.
Secondly change the oil using a vicosity suitable to ambient temperature in which you ride. I personally use ATF Type F and change it often. @ a 1.59 a quart I can change it frequently. I've experienced better shifting and less clutch noise using ATF Type F. I you don't like this idea, use what is recommended by Yamaha, Yamalube. Great oil but a bit pricey in comparison. Whatever oil you use, change it ever 2-3 rides. You'll see improvement and your clutch will survive a bit longer.
Matt's advice is probably the FIRST thing to do.