not sure what you mean about the drum, but letting us know the model you've got will help us help you. All the ones that I've taken apart have a clutch 'drum' part as part of the transmission, so it stays with the tranny when you remove the powerhead. The clutch itself is screwed onto the crankshaft and often has a set screw to hold it in place (whether it's really needed or not).
If grease is coming out bad, just add a little more to the tranny, re-seal the tranny halves with RTV if you must to ensure nothing with leak ever again, and button it back up. Leaking grease shouldn't have anything to do with the clutch. If it's an older model and you have it apart you may think about replacing the springs while you're in there.