The gemara in Nazir 53b has a machlokes when an adult cuts off the pei'os of a kattan. R. Huna holds that he is chayev, but R. Adah holds that the makif (barber) and nikef (person getting haircut) go together - whenever the ni'kef is not in violation such as a child (the steipler proves from here that we view a child as one who is not at all obligated, rather than just exempt from the punishment), the makif is also not in violation. However, Tosafos is unsure about the reverse case. Tosafos suggests that even according to R. Adah, we only exempt the makif when the nikef is not a bar chiyuva, but when it is the reverse we don't exempt the nikef just because the barber is not a bar chiyuva. Tosafos proves this from the fact the gemara in baba metziah 10b (in the context of shliach l'dvar aveira) not exploring the possibility of a jew who tells a goy or child to give a haircut to another adult jew. Tosafos holds that if Reuven would tell a goy to give Shimon a haircut, Revuen would be in violation (according to the opinion that we say shliach l'dvar aveira when the shliach isn't a bar chiyuva). But, how can a goy serve as a shliach to make Reuven chayev - a goy is not included in shlichus and cannot serve as a halachic agent?
The Mitzpeh Eisan answers that we must be speaking about a case where the goy is a worker. Even though we don't allow shlichus by a goy, there is a concept of יד פועל כיד בעל הבית which would be a usable concept to make Reuven liable for the goy's action.
The Nesivos HaMishpat 182:1 (quoted by cheshek shlomo) explains that the concept of not having shlichus for a goy only applies when by breaking the shelichus, it will prevent the action from being done. For example, if one appoints a goy to be a shliach to marry a woman or take teruma, we apply the rule of אין שליחות לנכרי because by breaking the shlichus the marriage and teruma would not take effect. But, when the action is not reversible, such as this case where a goy cut of the pei'os, we wouldn't accomplish anything by breaking the shelichus. Since breaking teh shelichus won't fix the problem, and all the shelichus is needed for is to attribute the action back to Reuven who told the goy to do cut off the pei'os, we consider even a goy a shliach and Revuen is chayev.