When you really get down to it, mummies in fantasy are basically liches with bandages, usually awakened due to someone pissing them off rather than for world domination. They are the preserved remains of kings who were worshiped as gods (more often then not in these stories) and if the power exists to make them move again then it only makes sense for them to have other powers of vengeance. I'd see mummies as either masterminds behind supernatural attacks, or used as some kind of superweapons by the other monsters.
For instance, they bring a sarcophagus to battle, and when the human resistance starts becoming problematic, BAM! unleash the mummy. They'd make sense as some kind of melee tanker, because in the classic mummy movies they were always implacable, indestructible beasts, not resting until they got their vengeance.
If you're looking for ranged attacks, and XCOM parallels, vampires could probably take the place of psionic enemies. It might be better to treat them as classic vampires, with all the weird powers, rather than humans on steroids with a craving for blood. In battle, they probably don't have time for a full-on turning your guys into undead slaves, but they could probably hypnotize them.