How do I loosen and then re-attach threaded PVC cleanout plug?
It is likely that the "putty" you see is actually pipe thread compound, or pipe dope, which is appropriate for most threaded pipe fittings. You should be able to use an adequately sized pipe wrench to unthread the plug without too much difficulty.

NOTE- there is a chance that someone used the wrong compound, as many are not approved for use on plastic pipe because the solvents in the compound can soften and damage the plastic. There is also a chance that someone used some other stuff (hopefully not glue). The only way to find out is to try to remove the plug.

Consider removing the compound and using teflon thread tape when you reassemble the fitting, or ensure any compound you use is approved for use on that plastic pipe (looks like PVC).