The Mutated Varkid is essentially a weaker form of the Badass Varkid. The reason why these are so dangerous, however, is because any Varkid can become one of these. If you deal significant damage to a Varkid but don't kill it, it may enter into a pod for a few seconds, after which it will come out as either this Mutated Varkid or the rather unusual Chubby Varkid. During this metamorphosis, you can kill the Varkid in its pod quickly with a few hits and it is advised that you do (except during the mission "Mighty Morphin'") because you will get more XP and loot than killing the morphed form.
Because each Varkid is a potential Mutated Varkid with nearly the power if not the toughness of a Badass, the best way of dealing with them is to not create them in the first place. Try to focus on one Varkid at a time lest you end up with an entire nest of them. If all else fails, fire weapons are your best bet for getting through their large health bars.