"用投石器投掷" can be translated as "to hurl (something) with a catapult" or "to launch (something) using a catapult".
Here are some example sentences to illustrate the usage:
* They used a catapult to hurl stones at the enemy's fortress. （他们用投石器向敌人的要塞投掷石块。）
* The soldiers were trained to launch projectiles accurately with a catapult. （士兵们接受了用投石器准确投射弹药的训练。）