Hi

It sounds like your clutch isn't properly disengaging, also known as dragging.

Older bikes such as my XS650, Z650 etc have a second method of clutch adjustment.
This is for the free play of the mechanism that the engine end of the clutch cable goes to, and the procedure is typically:
Put as much slack in clutch cable as possible.
Remove small cover from left side engine case.
Slacken loc nut and screw the screw in until it just touches mechanism behind it.
Back screw off half a turn and loc the loc nut.
Reset cable slack and refit cover.

Now the XT600 doesn't have such an adjuster accessable fron left side engine case, but loking in my Clymer manual they appear to have a screw and loc nut at the other end of the clutch push rod,in the clutch basket pressure plate, accessable by removing the right side engine case (which holds oil)

I havent seen a procedure for setting this on the XT, but it might be worth checking it's setting and trying half a turn out if it isn't already.
And while the case is off, I would take the plates out of the clutch basket and check how grooved the slots in the basket are. Ideally they should be no more than polished.
I would also chech the push rod and any ball bearings.
You don't need to remove the clutch basket to do this, but you will need to use a new gasket when you refit the cover, and possibly drain the oil from the engine too.

Good luck

Mark