This is a traditional chantey as well as a tavern song. Earliest date for this song is recorded as 1841. Each verse is another unpleasant answer to the question, "What do you do with a drunken sailor?" and this is often used as the title. Some of these solutions would be fatal.
Additional verses:
Throw him overboard and drag him on the anchor

Tie him to the topsail while she's yardarm under

Feed him to the sharks til the bones is floatin'

Hang him from the mast as a Jolly Roger

Give him a dose of salt 'n' water

Give him a taste of the Bosun's rope-end

Put him in a dress and throw 'im to 'is shipmates

Here are some additional, modern additions:
Sever his dinghy, make a mini-series

Make him the captain of an Exxon tanker

Put him out to pee in the poison ivy