I am a rising senior interested in mechanical engineering, but my passion is in jazz saxophone performance.
What is the reality of a dual degree at Cornell involving these two areas of specialization?
It is possible to get a five-year dual degree in engineering and arts & sciences: http://as.cornell.edu/concurrent-degree
That said, the undergraduate music department at Cornell is not very large; your degree would just be in “music,” not in jazz or in music performance or anything like that. If I were you I would consider majoring in mechanical engineering and doing a minor in music.