Yes. You can be separated for Commission of a Serious Offense under paragraph 14-12c, AR 635-200.
The definition of a Serious Offense IAW with paragraph 14-12c, AR 625-200 is:
Commission of a serious military or civil offense, if the specific circumstances of the offense warrant separation and a punitive discharge is, or would be, authorized for the same or a closely related offense under the MCM.
In plain English, if the reason for separation, if taken to courts-martial could result in a Bad Conduct or Dishonorable Discharge, then the offense qualifies as a serious offense.
IAW the Manual for Courts-Martial (MCM), the maximum punishment for Driving Under the Influence is:
DUI causing personal injury: Dishonorable Discharge or Bad Conduct Discharge, 18 months confinement and forfeiture of all pay and allowances.
DUI not causing personal injury: Bad Conduct Discharge, 6 months confinement and forfeiture of all pay and allowance.
Additionally, if a Soldier receives a 2nd DUI within a career, then the following applies IAW ASAP Regulation, paragraph 3-3, AR 600-85:
Any Soldier who is convicted of DWI/DUI two times during their career shall be administratively separated unless retained by the first GO in command who has a judge advocate or legal advisor available.
If you are processed for separation, you must be provided the opportunity to speak with legal counsel at your services Trial Defense Service office.