A stiff putty knife and careful use of a hammer would be my first try.

Thank you Chandler. The exterior is aluminum siding. I will post a couple of photos.

Cutting from the inside is a bad idea, you will need to cut from the outside so that you can actually see what you're doing. And that's only if you have enough room to slip the blade between the j-channel and the door frame. Generally the safest way to remove a door like that (and not do any damage to the siding) is to remove the sliding and fixed panel, and then cut the jamb into 2 halves... inside half and outside half. You do this along one of the extrusion edges- there is usually one that lines up exactly with the nailing flange. (usually about 1 1/4 behind the leading edge of the frame) Starting the hole is the hard part... and cutting straight takes some practice. But you should be able to reciprocate behind the nailing fin, cutting all the nails that hold it to the wall. (you will cut the nails that hold the j-channel too but don't worry about that) Once all the nails are cut, you can basically collapse the whole frame in on itself, pulling the nailing fin out from behind the siding. And believe it or not, the best blade to use for this is an aggressive wood w/nails blade, not a metal cutting blade. Aluminum will gum up the tiny teeth in metal blades. Best blades are the Milwaukee Axe blades.