How do I keep my 89 yr old gma with alzheimer's from taking her cast and sling off? She has a fracture, dislocation and stitches. 3 ER visits 1 day.

Pain control . For behavioral disturbances of dementia the best technique will be reorientation and distraction, to focus in something else, but before any pain or discomfort should be addressed and treated this will require a lot of supervision. Pharmacological treatment can be considered in some cases but should be tailored individually based on other health problems and other medications being given.
This is a hard one. I am assuming your gma is so confused that she is unable to understand the need for the cast and the sling. The first thing to do is determine if she is trying to make the arm hurt less, that is, she is in pain and she looks at those 'things' on her arm and says to herself 'get these off they hurt'. Try controlling the pain.