You cannot occupy the same square as another creature (unless there's enough of a size difference, which I doubt there was in this case). Technically, this includes if you're prone. If you were able to act while prone, then the mummy would not have been able to enter your space at all. Obviously, since you were dead (and thus counted as an object, not a creature), that issue wasn't relevant. But, for future reference, being prone isn't enough to allow an enemy into your space.
Personally, as a DM, I would rule that if there is an adjacent empty space, you can take a 5ft. step during your move action to stand up (though standing would still provoke). Barring this, there are two options you have, via RAW:
Crawl up to 5ft while prone, then stand up. It seems you couldn't have done this, since there were no empty spaces to crawl to. If an adjacent square was occupied by an ally, then you could double-move to crawl 10ft. You combine movement totals with a double move, which is important since you can't end your move occupying the same space as another creature, even an ally. This is, of course, assuming that there is an empty space within 10ft...
Second, you could attempt to bull rush the mummy out of your square. This would be inadvisable, since you'd suffer some hefty penalties (-4 to the attack, plus you'd suffer an attack of opportunity anyway). With no adjacent squares empty, you'd have to make two successful bull rush checks, against the mummy and then against whoever's space you pushed the mummy into. I believe that the second check would take a -5 penalty as well.
So, in the end, your best bet is to crawl away and hope for some luck.
Barring a DM ruling that makes things easier on you, of course.
Oh, and for the record: since you can't occupy the same space as another creature, I'd rule (again, me personally, since there are no hard rules on this) that the mummy would have to take it's next opportunity to move out of your space. If it was unable to (like the situation you described) then I'd give it penalties as if it were squeezing, since it's got an active being taking up most of its space and trying to get it the hell away. Of course, you'd take those squeezing penalties as well, since the same applies to you... [Edit: on second thought, I'd more likely just have it automatically move into the first empty space that opened up, without using actions or causing opportunity attacks. Since it's really a sort of nebulous, "you're being defensive even in-between turns" action on your part that's making him move.]
On a side-note... these sorts of discussions are the main reason I've been drifting more and more toward systems that focus on cinematic combat rather than tactical combat...
