I was put on probation for one year for a dui. Last month the year was up. I have not completed all of my community service. Can I be violated since my probation period has already expired.

Yes, most certainly you can be violated. What is your excuse for not completing your community service? Other than being in a hospital with a serious problem, I doubt the judge will take too kindly to you ignoring this most crucial part of your sentence. It does not matter that "last month the year was up" either. What matters is that you complete your community service ASAP or you can and will be violated and brought before the judge at a probation violation hearing. If I were you I would do whatever is necessary to complete the community service even if it means missing work for a few days and doing the community service work on the weekends. Right now you are technically in violation. It's just a matter of time before you are either picked up and wait for your probation violation hearing in jail or you do what is necessary to finish off your imposed sentence requirements now. The choice is yours for now, but that will change very quickly once you are found out.