Acne

Reducing acne can be a common argument as a reason to go vegan, but there is no clear evidence other than anecdotes that a vegan diet is better for acne prevention or treatment.

Veganism and Acne Arguments

"Go vegan to cure acne" is probably not a good argument to make at this point in time. Making this argument could cause unintentional psychological harm to vegans with acne thinking they may have done something wrong, or to people trying veganism who may feel betrayed (and get a bad impression of veganism) when promised miracles don't happen.

A possible rebuttal to this position might be that if you argue "go vegan to cure acne," this might get people to go vegan who might learn about the ethical arguments and stay vegan despite continued acne (similar to other health foot-in-the-door arguments), or the acne may clear up by coincidence.

There is a caveat to this strategy, though, in that when we don't know which effect is more pronounced and whether there is net harm or good from misinformation, lying isn't the best policy and erring on the side of honesty is the smarter option even if you don't have any ethical qualms with lying due to the possibility of blowback from lies being discovered and making it hard for people to trust other information.

Dairy Related Acne

There is some limited evidence that dairy causes acne, but that may only be for some people (it could be different from person to person). Some of the proposed mechanisms of action are hormones in the milk, milk proteins themselves raising HGH endogenously, and the high levels of iodine from iodine based sterilization in milk production.

B12 Related Acne

Only very large (unnecessarily large) supplementary doses of some vitamins and minerals pose health-risks. In extreme doses, B12 supplementation can cause mild acne-like symptoms (if you experience those, it's a good idea to cut back a little).

On more moderate doses, you will see no side effects. Mild acne-like symptoms from large doses of B-12 (which go away when the dose is reduced) aren't really a health risk, but it's pretty well known and often mentioned in vegan nutrition guides.

Treatment

Taking a very small zinc supplement (around or below the RDA of 10mg a day) might help if you are low on zinc (or eating more zinc rich foods like pumpkin seeds).

However, effects of diet and even supplements are likely modest compared to medical intervention. Can you improve your symptoms a little with diet? Probably. Should you do that instead of taking medicine? No way.

Acne poses a risk of disfiguration from scarring, which can cause lasting psychological harm, and the scarring is pretty much irreversible. So a policy of "wait until things go wrong then go to mainstream medicine" is not ideal.