Use this expression to talk about things that you shouldn't do because it would be wasteful:
There's no sense in asking him; he doesn't know anything.
There's no sense in throwing away a perfectly good pair of shoes.
In the first example, it would waste time to ask the person who doesn't know anything. In the second example, it would be wasteful to throw away the shoes.
In the sentence "There's no sense in beating yourself up over it," the speaker wants to say that thinking about a mistake again and again is a waste of time. It makes the person upset but doesn't have any positive results.