I was playing against some t50 guy using this "rage quit deck" (Mr Sexington's?), which basically works as stated, killing every creature you have and healing for insane amounts of hp. I started with an elf/FFQ combo in my hand and while I was setting it up he got a thorn carapace out. I thought I might get a mutant with steal if I could stop my creatures from attacking with sundials. First mutant: 8/4 cockatrice with steal. EPIC WIN.
That much epicness needs explanation though: the game lasted so much (mainly due to him healing in ridiculously numbers) that I managed to steal at least 15 permanents from him (6 SoGs, 6 thorn carapaces, one Eternity, 2 mind gates, hourglasses...). His healing capabilities were so intense he got to almost 500 health (SoDs, Stone Skin). Thanks to his mind gates, I also benefitted from those spells and EM'd him at 375 hps (he decked out LOL). Due to having 375 hp + EM, I won 172 electrum from that fight.
That cockatrice might not be a really weird thing, but it is at least the most epic mutation ever, in terms of usefulness.