Joseph's mummy has not been found, but there are many "Bible Era" mummies that have survived.  The Egyptian Museum's Royal Mummy Room has a very nice collection, including the mummy of Ramses II.  Recently, the mummy of Hatshepshut has also been found and examined.  If we date the Exodus at 1446 B.C. (which is internally consistent with the biblical narrative) she would have been the princes who fished Moses out of the Nile River in Exodus 2.

For more on mummies, see my Bible Blast titled "Joseph's Mummy," as well as my article, "Egyptian Myth Busters."  I'd also highly recommend Prof. Bob Brier's Teaching Company course, "The History of Ancient Egypt."  You can get his 48-lecture course at www.teach12.com.  It is excellent.