I did this job once myself (well, with the help of my father.)
First, I 'separated' the portion caulked to the wall with a utility knife (being careful NOT to scratch the tile.) THen, as I pulled UP on the door structure, my father ran a utility knife along the caulk, end-to-end, and then start from the beginning end again, until it basically came up. Just an idea to get you moving.
My best to ya and hope this helps.
PS: if the caulk is hard, you may want to remove what you can to get to the 'soft' caulk underneath. then it will be easier to 'cut'.