Do you mean, by "hand mixer" a submersible mixer? (Like a plug in drink mixer?) If so, yes! If it's a rotary, I don't think it would work well. You'd mix it well enough, but it wouldn't give you the puree you're looking for.
It doesn't work quite as well as a proper food mill or a blender, but pushing it thorugh a basic sieve seems to work pretty well for me - I once even sieved soup, very slowly, though a tiny, tea-strainer-sized, sieve from IKEA because that was all I had around. (IKEA's "toy" cooking utensils for kids are really well made!)