Discharge has more than one meaning and the other one is pretty uncomfortable. Not to dissuade you, but please consider it before doing anything drastic.
Which is why I wondered how it would be received in the non-service communities. When you say "Discharged" for those who had been in the military or peace corps they think of what I linked but I wasn't sure if our culture was steeped enough in martial tradition to have the same connection. I know there aren't as many war movies as there once was and the percentage of people who choose to serve in any fashion (LE, Fire, Med, Military, Volunteer) is shrinking.