Also saturated fat is essential to testosterone production, so if you cut out a lot of it your diet then testosterone and your bodies natural steroid and growth production will slow down, large and sudden calorific deficits also have the same effect as well as prolonged cardiovascular exercise, all of these mean less testosterone and less testosterone means less skin problems.
There is an argument that items that are high GI in nature (ie processed and sugary foods) will spike insulin and blood sugar levels and cause acne but anecdotally I've been on low GI diets for months and never noticed a single change in my skin.
Heavy lifting and eating appropriate saturated fats (although not unhealthy) can have the exact opposite effect and increase testosterone levels.