If you've have a salivary gland stone do you have an operation to remove it?

Sometimes. Just like a kidney stone, it may be possible to pass the stone in your salivary gland duct. Surgery is possible if you cannot pass it on your own.
Salivary stone. Depending on its location, it can be removed in the office. If it is located deep within the gland and causing symptoms more aggressive surgery may be required. Some centers are using experimental lithotripsy to deal with salivary stones.