Normaly, death is much like a nap for a mummy, as they can inhibit their bodies again and again. However, when the body of a Mummy is destroyed on an atomic scale (such as standing within a nuclear blast), the mummy is completly destroyed- it can not regenerate and their spirit goes on like that of every other mortal. Other means to truly kill a mummy usually involve high and complex magic, that affects reality itself and is able to wipe out existences as if they never had existed.
It is also possible for a mummy to end her existence by themselves. Osiris doesn't force eternal life on anyone