Is saw dust in the eye dangerous?

Possibly: You can get a scratch and perhaps an infection from sawdust. Most of the time, it just causes irritation. Use water to flush the sawdust out. If this does not work, see a doctor.

Usually not: Sawdust commonly enters the eyes of those working with wood and near those working with wood. With each blink, most exits. Most saw dust is inert and will not be toxic in itself. The major harm would be for instance if someone is drilling in wood, creating sawdust of course, but hitting a piece of metal which flies into the eye.