I would start with the Utah State Historical Society Burials Database at http://history.utah.gov/apps/burials/execute/searchburials
They do have a listing for John Mortensen died 23 Apr 1951.
Since he was buried in Levan, I would check the Nephi Times News for his obituary www.nephitimesnews.com
You will probably have to contact the Nephi Public Library to find back copies of the newspaper.
I think some of the Nephi Times News are in the microfilm collection at BYU, but I'm not sure.
Since he lived in Salt Lake when he died, I would also check for an obituary in the Salt Lake Tribune http://www.sltrib.com/
and the Deseret News http://www.deseretnews.com
Many obituaries for people in Nephi/Levan are also printed in Provo's The Daily Herald http://www.heraldextra.com/
so you may find one there. It probably depends on where relatives were living at the time.
Also, you can try looking for microfilms at www.familysearch.org
to see if any of the newspapers have been microfilmed for the time period you want. You will need to click on the Family History Library Tab and then select the Family History Library Catalog.
Some of Utah's newspapers have been digitized and are available online at http://www.lib.utah.edu/digital/unews/
Also Utah Archives have Death Certificates online at http://archives.utah.gov http://historyresearch.utah.gov/digital/archives.htm
does have a copy of his death certificate.