Cobweb says he never took Rickwalker's neck, but then how did Paranoia knock his head off?
The whole thing was a Mind Screw by Cobweb meant to make Rick think Sleepwalker was evil. Otherwise you could just as easily ask why being decapitated didn't kill Rickwalker on the spot.
Considering Sleepwalker heals from practically anything while in the Mindscape and the Sleepwalkers send the more dangerous denizens to remote regions instead of dealing with them permanently, it seems like the residents of Mindscape are practically immortal. Even Cobweb was beheaded by Rickwalker and it didn't seem to bother him at all.