He began his senior career at Bohemians in the summer of 1994 after playing youth football for St. Kevins Boys. Mick became Bohs' youngest keeper ever when he made his league debut against Dundalk on August 28 1994 at the age of 18 years and 297 days. He spent 8 years at Bohs until he moved to Dundalk F.C. in the summer of 2002. Dempsey then moved on to Longford where he currently serves as back-up goalkeeper to Seamus Kelly.
He was capped by Ireland at Under-21 level for Ireland in March 1996 against Russia and won the Soccer Writers Player of the Month Award in January 2000 for his performances for Bohemians that month.