In a combat situation how does the Dungeon Master determine if a limb of someone has been cut off as opposed to just receiving general damage?
Barring third party documents, Dungeons & Dragons has not considered critical damage in terms of permanent limb loss, etc. Other systems have whole charts for them, but Dungeons & Dragons never went that direction. Some of typical methods of determining major critical have been d100 charts, double 20s and then a d6, d8 or more limb loss simple result and many others. One of the methods I liked to use was double 20s, where a second [Critical Hit] had to occur, after a [Critical Hit] was rolled, and then a d100/ chart for results. This had broken bones and dismembered limbs, as well as concussions, lost facial features, etc. Only regeneration or major heal would repair these conditions. YMMV, but there are plenty of resources to use.
RuneQuest is a great system for this but as the poster above said, Dungeons & Dragons had not considered it. But let me go after what the original poster is asking.... How would you do it in Dungeons & Dragons, personally I would cut off a limb if that is specifically what the player is targeting and then I would put a certain AC modifier to the base AC of the monster to see if it was possible.
Its also easy to take off limbs from players that fall for certain traps. Having one arm or leg makes for interesting adventuring *wink*.
In the games I've been in I have only seen limbs taken off when it was targeted. For instance a portal trap, when the character puts their hand in it goes missing.