Most likely to be a cup with two weights with cork outer pads to grip on the inside of the cup. If they get oil on the cork a soak in meths, wipe off the meths/oil and the burn of the meths should do the trick. They are not usually adjustable.
I`m on my second unit, the first lasted around 17 years and when it wore out and I tried to repair it the parts were nearly as expensive as a new unit.
Depending on how old it is and how much use it gets, you may get it going with a few new bits, but it will be a "Forth Bridge" or "Harry`s Broom" if you`re not careful. At least that was my conclusion when I tried the exercise.
Oh, there was no clutch in mine, the drive is a bit like a car windscreen wiper, worm gear and eccentric plate.
I think some people are confusing the clutch with the sort of mechanism used in a car, where the clutch also has a cushioning function.
In my experience, on this type of rotating machinery (the reciprocating movement is introduced after the clutch) the clutch is simply two metal plates with dogs, usually smooth sided, one of which, the output side, is spring loaded, adjustable with one, or maybe two, screws.
It is this adjustment which is not readily apparent.
If the output was via any sort of gear train, or rack and pinion, the teeth would strip on overload and cutting action would cease.