DUDE-
First of all you can ask your doc everything without taking into consideration wether or not he will think you are crazy- I just don't think he will do it!!!
A) Evidence based medicine- nowhere is it found that amputation is therapeutic in psoriasis.
Psoriasis is believed to be an autoimmune disease and as such removing the "limb" wouldn't necesarily take care of it!
B) Also intuition- amputation sounds a bit much! You wouldn't cut off your leg in a case of sprained ankle- although it would probably heal it.
C) Because of the forementioned statement- a doctor could lose his license doing something like that.
D) With respect to the finger being your finger- doctors are bound to a different code of ethics- just like they can't aid in suicide or do all sorts of funky things in the field of cloning they can't amputate a finger because the patient so desires.
E) I don't want to offer medical advice through this forum but it sounds to me like you should get a good dermatologist- make sure it's psoriasis, usually it appears on extensor surfaces (not the finger) and usually it comes in flare ups. Maybe you have something else that hasn't responded to anti-psoriatic meds.
F) With psoriasis there is also a large emotional factor- just chill!!! It's not the end of the world!!! Relaxation is actually therapeutic because psoriasic flare ups is associated with stress. If your lesions are just on your finger then you have it good- it could be a lot worse so just relax so that it won't get worse!!!
Hope this helps