This cartoon casts Theodore Roosevelt as the fictional character Jack the Giant Slayer from children's tales. In the role of the Giant we have J.P. Morgan and others, some of the Captains of Industry or Robber Baron's depending on who is writing. You probably noticed their names are on the hems of their clothes.

Roosevelt had a public stance as a Trust Buster. The trusts were large, monopolistic corporations such as J.P. Morgan-Chase and Standard Oil. Roosevelt worked to break up those companies, at least nominally for the benefit of the little man, thus the sword which says public service.

The giants are J.J. Hill, J.P. Morgan, possibly William Proctor Gould Harding, and two which I cannot read in back. Their names are on their headband and blue shoulder pauldron respectively.

EDIT: I did some quick work with Tineye reverse image search and I found some more information on your painting.

This website has a collection of more cartoons from Puck Magazine with information on them. Yours is down near the bottom. The people pictured in your painting are George Gould, James Jerome Hill, John Pierpont Morgan, Henry Oxnard, and John Davison Rockefeller.