Say, young feller vatch de tome. I'm de tome, you gant buy id. I'm a good ting but don't push me, see! Pulitzer

The writing is a phonetic rendering of Jewish or German-inflected English (Pulitzer was Hungarian-American and Jewish). In this case, de tome probably means "the tone" - Hearst being a major rival and competitor.

The context: the comic ran 29 June 1898 in Vim. The political cartoon was about the rivalry between publishers Pulitzer and Hearst, who were locked in a circulation war and yet both were pushing for war with Spain, which led to the Spanish-American War. They are both dressed in yellow as a hallmark to the "yellow journalism" that both regressed to - and more specifically, they are dressed in the same way as the early newspaper character "The Yellow Kid," which had appeared in both Pulitzer and Hearst's papers.

You can find a better image of it here: https://en.wikipedia.org/wiki/File:PulitzerHearstWarYellowKids.jpg