You remove the HS from the CPU while the CPU is still in the socket. You do not pull unless you know for sure the type of thermal stuff that is on there. Some thermal pads can stick to athlons or durons (die type) tightly enough to pull the CPU out of the socket if you try to pull. the only case where twisting is not recommended is if thermal adhesive was used. In that case you have to pull the whole thing out and figure out what kind of solvent is needed - sometimes allowing the CPU to get hotter than normal for a few seconds will allow a thermal adhesive's seal to be broken.
. First, the HS needs to be released from any mounting clips, etc. as it has to be totally freed from the mobo and any mounting stuff out of the way for freedom of movement. The twisting should be firm but gentle - a couple of degrees back and forth should release any pad or grease as they have almost no shear strength. If you twist more or harder than that, then you just don't get the concept... Sorry Charlie.
.bh.