Around the ages of 2 to 3 years old (and sometimes older), alpacas grow sharp, dangerous fighting teeth. In females and geldings you do not have to worry about them as much as you do for studs/males that use them to attack others males and could possibly harm a female during the mating process.
The process may be intimidating, if you do not wish to be the one cutting the alpacas teeth, your vet would more than likely do it, or ask around to other alpaca farms in your area and see if they would help you out with it.
Shown in figure 1 you see a diagram of the skull of the alpaca/llama and where the teeth are located. The fighting teeth are not to far back so you can easily cut them with just someone opening the mouth and you going in for the cut! But technically you are sawing their teeth off, with obstetrical wire.
In figure 2 is a lovely diagram of how the process would be done, you take the obstetrical wire, put it behind the tooth and pull one side, then the other and so on until the tooth it cut or sawed.