Mark up is a phrasal verb. English has many of these. Mark up can have a different meaning than mark, though it is related in meaning.
The second word in a phrasal verb sometimes doesn't have a lot of meaning in itself, or clear relation to the first word, and in those cases is just a signal to change the meaning of the first word.
Up appears as the second word in a lot of phrasal verbs, e.g. make up, get up, shut up, write up, etc.
You are correct that up can mean all with certain verbs (e.g. finish up). It can also function as an intensifier (e.g. clean up), or mean something like "on it's own" (e.g. clear up).
To add confusion, sometimes a two-word verb can have a separate meaning phrasally, yet still be able to be used non-phrasally. A lot of times the difference in meaning depends if the subject is a person or a non-person.
Me and my girlfriend are breaking up. (To break up = to end a relationship)
The snowball broke up in the air when I threw it. (Literal meaning of break = to disintegrate with up meaning "on it's own" or an intensifier).
I told that annoying person to shut up. (To shut up = to stop talking)
I shut up the cellar door. (Literal meaning of shut = to close with up functioning as an intensifier.)