If a soldier commits a crime and receives a sentence, is he dismissed from service?

YES, fired.

Grounds for dismissal from military service during martial law are defined in the Law "On Military Duty and Military Service" No. 2232-ХІ of March 25, 1992.

According to the aforementioned Law No. 2232-ХІ, one of the reasons for the dismissal of a serviceman from the Armed Forces is the entry into force of a court verdict punishable by imprisonment, restriction of liberty or deprivation of military rank.