This requires you to play the Zealot class with the charge ability. Mutants, despite their appearance, are actually quite squishy.
Prep:
Any big weapon will work well with this, but I personally recommend the thunderhammer, the heavy eviscerator, or the relic blade. The Thunderhammer can charge up with the special attack, and combined with the bonus damage from the charge, can instakill the Mutant with a well timed light attack. The eviscerator, however, requires a charged attack, but you can hold that until are right on them. The Relic blade can be charged to boost damage as well, similar to the thunderhammer.
How to do this:
The Mutant roars when it arrives on the map. You can hear it get louder as it charges into view. When you have line of sight, use the charging blitz to dash forward and hit the mutant, killing him. I recommend easier difficulties, but there are lower spawning rates the lower the difficulty. Two or three is the best balance, I found. Just... don't highlight them, because others will just shoot the mutie before you can get to them.
The rest just requires skill and timing. Good luck, varlets!