tdracer - Many types of explosive are quite stable over a long period of time - however some types do decompose into more unstable forms and become very dangerous to move after decades of inactivity.
Amatol is a mixture of TNT and ammonium nitrate and is therefore relatively stable. I won't go into the fine details, there are too many suspicions raised if you access anarchy sites, and instructions on composition and manufacture of explosives.
Yes, the de-activated bomb is removed from the site and taken to the likes of a weaponry range for destruction by a suitable small initiating explosive.
The important factors are precisely identifying the model of munition, obtaining the technical specifications of the munition (nearly all types of military munitions specs are still on record) - and most importantly, identifying any "anti-handling" devices that are likely to have been fitted. "Anti-handling devices" are those devious devices designed to kill anyone trying to de-activate the munition, and they can be exceptionally dangerous.
In SVN, M16 anti-personnel mines ("jumping jacks") were often placed in the ground with a hand grenade set below the M16 casing with the pin removed.
The fly-off handle of the grenade would be retained in position, thus keeping the spring-loaded striker from initiating the activation of the grenade.
Unwary sappers would de-activate the M16 fuze (a relatively simple operation), then lift the M16 from its resting place in the ground, and "BOOM" - the unwary sapper was often seriously injured, and occasionally killed, by the grenade going off, once the pressure came off it.