Generally speaking it means to "take attention away from" or to direct attention elsewhere. For example: "Foul comments and careless jokes between friends ensue, which takes emphasis away from serious remarks." Attention is taken away from the serious remarks, and all anyone hears are the negative remarks. In that exact sentence it is hard to say without context. I would guess the writer or speaker is trying to say that your attention is taken away from meat based food, since you are on a strict diet.

Hello Italkian friend. How are you? It's nice to meet you. I suppose the phrase means that once you become a vegan, you will have to abstain from a certain amount of food that would contain animal meat or anything else forbidden by it. I hope this will do! Cheers!