If I create a token using Purphoros's Intervention's first mode, and then I mutate a creature over it, do I still sacrifice the resulting creature at the next end step?
Yes, you still sacrifice the creature.
The rules for "Merging with Permanents" say this
723.1. One keyword causes an object to merge with a permanent. See rule 702.140, “Mutate.”
723.2. To merge an object with a permanent, place that object on top of or under that permanent. That permanent becomes a merged permanent represented by the card or copy that represented that object in addition to any other components that were representing it.
- 723.2c Because a merged permanent is the same object that it was before, it hasn’t just come under a player’s control, any continuous effects that affected it continue to do so, and so on.
Since the merged permanent is the same object as the permanent you had before you cast the creature with mutate on it, any instructions that referred to it before still refer to the merged permanent, including the instruction to sacrifice it.