@Walt
After some thought, I realized that there would be instances where you would want to push enemies away, like if you were under threat of a ship that wanted to ram you. Or if you were a kiter and wanted to keep an enemy away, or counter their tractor pulling. (Tractor beams are a counter to tractor beams??)
So the way you guys were proposing to control whether it pushes or pulls was that there would be a slider that sets the range you want to keep the enemy at. But I think that's overcomplicated. Imagine trying to manipulate a slider during a fight. It requires too much precision, plus knowledge of the range numbers.
So instead of a slider, just do a binary toggle - pull or push. In pull mode, it draws the target in until it is close, maybe a little beyond the range of shield projection, since you wouldn't want to be pulling them inside your surface-mounted shields. Then again, would that be close enough for the short range weapons, such as the proposed buzzsaw? In push mode, it would push them out to the max range of the beam.
Another interesting thought: if tractor beams operate like a turret, and if they can target individual parts to apply their force to instead of the entire target, then you could have one tractor beam target one side of the ship with pull, and another target the other side of the ship with push. This could force the target to begin to rotate, misaligning their intended thrust vectors and worse, bringing their weaker sides to bear for your weapons to chew up.