(The following is all from an American English perspective, specifically California. I think some of the fine distinctions here are subtle, and might depend on dialect.)
"Rip up" primarily means "destroy by tearing", normally only when referring to paper and similar things that can be torn. ("Tear up" is a synonym.) It can also be used metaphorically, usually for the sort of things that might be written on paper, even if there's no actual paper involved. I.e. "I had to rip up all my work and start over," or "If you do that we're going to rip up the agreement."
"Rip up" or "tear up" can also mean "remove by tearing or pulling in an upward direction". For example, one can "rip up" a floor when renovating a house. "Rip out" would generally also be fine for this usage, and is more generic. (I say "generally" because I can't think of any counterexamples, but they may exist.) I would say this is the usage of "rip up" that you're seeing in the book -- one removes the trees by pulling them upwards, out of the ground. The book could just as well have said "rip out", but "rip down" would sound strange.
"Rip out" primarily means "remove by tearing or pulling". For example, one can "rip out" stitches in fabric, or "rip out" pages from a book. ("Tear out" is a synonym.) Usually the part being "ripped out" is not desired, and will be discarded, but not always. (You can rip a piece of paper out of your notebook, because you want to use the paper to write on.) It's less restricted than "rip up" in terms of materials -- for example, you can rip a fixture out of a wall. (But only if it extends into the wall. If it's just attached to the surface, you would say "rip off". See below.) On a larger scale, you can "rip out" walls from a house when renovating. This can also be used metaphorically, for other kinds of removal. For example, you can rip out a section of an agreement.
"Rip down" and "tear down" generally just refer to destroying buildings, or similar large structures. You could tear down a house, or a bridge, or a monument. Ronald Reagan famously asked Mikhail Gorbachev to "tear down" the Berlin Wall. ("Tear down" is usually more idiomatic than "rip down". I don't think I've ever heard someone say "rip down", but "tear down" is used all the time.)
You could reasonably also use "rip down" or "tear down" to mean "remove by tearing or pulling in a downward direction", i.e. "let's rip down the ceiling of this room and see what's behind it." But I think most people would say "rip out" or "tear out".
For completeness, "rip off" is a little bit weird compared to the others. You can "rip [something] off the wall" (meaning "remove violently", similarly to "rip out" but referring to removing something from a surface.) But you usually wouldn't "rip off [something] from the wall". When "rip off" is used as a phrase, it's usually an idiom meaning to cheat or steal from someone.