Aside from the already present answers (and expanding on StoneyB's answer) this could originate from the fact that English is a Germanic language. There are many similarities between English and German and one of them is what in German is known as a "separable verb".
First you need a "separable prefix". An example is "an", a preposition meaning "at" or "on". In other contexts it can mean "on", such as describing a light.
You then take a verb (such as "machen", or "to do").
Merging the two, you get "anmachen" meaning "to turn on"
Similar to how there isn't a German verb for "turn on (a light)" but instead there is a modified version of an existing verb, there isn't a single English verb for "to give up". You can think of this as being formed from "up" and the verb "to give", both of which have meanings completely irrelevant to the verb they form together.
I think you can say that "to beat up" is another one of these verbs. "To beat" means "to defeat" or "to strike" but with by adding this particle you can change the meaning to something closer (but not exactly) to "to bully" but not nearly as violent as "to beat".
The only way to know what these verbs with particles mean is by remembering them as you would remember any other word.