Turf-Cutter is a slur used to describe Irish in a derogatory way. Turf is peat moss, found in deep layers in Ireland. It was originally cut by most Irish farmers and used as fuel (an early form of coal). More modernly, it could apply to any drunk Irishmen working as greenkeepers, such as on golf courses.
The word Turf-Cutter is a racial slur that has been used historically to degrade and dehumanize irish. The word is still used by some people for this purpose, and it is seen as offensive and hurtful to irish. If you are unsure about whether or not it is appropriate to use the word Turf-Cutter, it is best to err on the side of caution and avoid using it in any situation.