Why do we use up as adverbs for verbs? For example, 'wake up', 'throw up', etc.
"wake up" and "throw up" are phrasal verbs.
A phrasal verb is a combination of a verb and a preposition, a verb and an adverb, or a verb with both an adverb and a preposition, any of which are part of the syntax of the sentence, and so are a complete semantic unit. Sentences may contain direct and indirect objects in addition to the phrasal verb. Phrasal verbs are particularly frequent in the English language. A phrasal verb often has a meaning which is different from the original verb.
Notice that "throw up" and "throw" have different meanings. "Throw up" means to "vomit", while "throw" means "to propel through the air by a forward motion of the hand and arm".
Bruno's right, they're phrasal verbs. Just think of how many phrasal verbs you can construct from "to get": get up, get down, get on, get off, get over, get under, get by, get through ...etc.
I imagine it must be tough for non-native speakers of English to learn these. I suppose you just have get down to work and put up with it.