Hard question to answer. If I say, "I am going to clean," it means the same thing as, "I'm going to clean up." It's mostly a colloquial thing.
In some ways, adding the word "up" might imply a general and broad application of the action. I'm going to "clean up" probably means you're making your whole house clean, where saying I'm "cleaning" might lead to the question, "What? What are you cleaning?"
In the same way, saying, "I'm ripping the paper," kind of implies a single or partial rip, where saying, "I'm ripping up the paper," means you're ripping it to shreds -- destroying it.
But if you just ignore the words "up" you won't be missing any meaning. It's mostly a meaningless addition to verbs.