Yes. It is a DQ for all military services per DoD Instruction 6130.03
http://www.dtic.mil/whs/directives/corres/pdf/613003p.pdf It is likely also on some of the services lists for 'no waivers authorized' but you would have to search for a link to those lists.
n. History of suicidal behavior, including gesture(s) or attempt(s) (300.9) or
history of self mutilation or injury used as a way of dealing with life and emotions.
Depending on your entry source (ROTC, Academy, HPSP, USUHS, Direct Commission, OCS, Enlist) you could try one of the DoDMERB consultant companies if you have $1000 to throw at it -- but they make no guarantees.