Can you give away or destroy artifacts?
There is no way to destroy great works in this case, they can only be destroyed if you capture them from an opposing civ. In the future you should just not make excess archeologists. If you do want to prevent your opponents from excavating an area (and have open borders with them), you can park a worker or other unit on the square where the archeological site is. You can also consider constructing a wonder with artifact slots, if there is one remaining.