There are two different principles to reduce or eliminate the sweating:
There are various surgical procedures aiming at complete removal or at least serious damage to the glands. The effect comprises only the area where the operation is performed. The trauma of surgery is generally more significant than in sympathetic surgery, the healing process usually much longer.
These methods are almost exclusively used to treat axillary hyperhidrosis.
Blocking or dividing the nerve that activates the sweat glands will result in their incapacity to produce and excrete sweat. The effect of surgery on the sympathetic nervous system is usually not localized, but covers a larger area on the body surface, which may result in increased sweating in other regions of the body as a counter-reaction, though more recent techniques aim at containing these side-effects. Sympathetic surgery is nowadays carried out with minimal invasive technique and, therefore, associated with minimal trauma and fast recovery.
With sympathetic surgery it is possible treating body regions where direct sweat gland removal is not possible (face, hands, feet).
There are also overlaps between these two principles. Curettage or aspiration of the sweat glands does not result in complete removal of the sweat glands (many of them are only partly damaged), but it also denervates the glands, as the nerve endings are torn from the gland.