In a relationship scenario if someone was bothering you you could "shake them off" or "shake it off". Meaning do not let yourself be worried or overly upset by what that person said or did and move on emotionally

"Shake him off" means the same as "Get him off you back". These both mean, "Get away from him" or "Get him to go away." When you're trying to "shake somebody off", it means you're trying to "lose them." As in, you don't want them to follow you, so you try to get away from them.