In the early 1800's mug originally means to beat up so then mugging was to attack by beating up. It was influenced by the slang term of thieves 'to mug' meaning to "fool or sucker". Put both meaning s together and you have a mugging modern style:-)

From The Maven's Word of the Day: The first word we need to consider is mug as a noun meaning 'a heavy cylindrical drinking cup with a handle'. This sense, first attested in the late seventeenth century (the late sixteenth century had an earlier sense 'a vessel of any sort'), is of uncertain origin, but is probably from a Scandinavian source. The sense 'a person's face or mouth', which is still current, is from the eighteenth century. It seems to be transferred from actual mugs that were adorned with grotesque faces (such mugs were common in the eighteenth century). (The sense 'to assume exaggerated facial expressions', not really germane to your question, is the first related verbal use, from the later eighteenth century.) The early eighteenth century brought us a sense from boxing, 'to strike in the face'. The group of senses that includes what happened to your friend stems from here. The earliest related sense is 'to assault with intent to rob, especially by grabbing in a choke-hold from behind', first recorded in the 1860s (and also as a noun in the same time period). Though many dictionaries stop here, the main current sense is often just 'to rob' (not necessarily with any implication of using violence). Striking a victim in the face does not ever seem to have been a specific aspect of this sort of mugging. Some other notable forms are the noun 'a photograph taken by the police for identification purposes', from the 1860s; the verb 'to take such a photograph', from the 1890s; the noun 'a low, crude fellow; lout; thug', from the 1860s; mugger, from the 1860s; and mug shot, from about 1950 (though mug-shooter is found in the '30s).