There is a plot point where a bad storm rolls through and there is a mudslide/landslide. After the storm, they find that the river has been dammed up because of the landslide and they are on the flooding side of it. I want them to work on undamming the river but was wondering about how realistic this would be with primitive tools. They have iron tools like shovels, pick axes and the like... but no explosives. they have oxen to move material out of the way, too... how dangerous would this be and how long would it take to clear?
Pretty much the entire UK canal system (nearly 5000 miles...) was built with hand tools, so it's entirely feasible. How long and how dangerous depends on what the material that has collapsed is. If the river is underneath a limestone cliff which has collapsed, there could be huge chunks of rock to try to break up which would take ages and be more hazardous, if a silty/gravelly bank has slipped in, it would be much easier, and once a channel was created the river would start helping by carrying a lot of the material away. Unless you are aiming at a bunch of geologists or civil engineers, just make it feasible and go with what suits your story.
