The Super NES version is a beat 'em up. In this version Sonic Blastman must save the Earth from diverse kinds of evil forces, from street gangs and terrorists, to aliens and robots and finally, an evil clone of himself. The fight starts on a construction site in Earth and ends up in outer space.
The game is only for one player. As in any beat 'em up, the game consists of defeating the enemies on screen before continuing in the stage. Sonic Blastman can punch, jump, and grab his enemies, too. He also uses a special attack that knocks any enemy nearby, but it dizzies him temporally. Another particular feature is the way Sonic Blastman holds his enemies: When he approaches his enemies, he is able to grab them in order to shake them and throw them back from him, or unleash a series of punches. However, if he punches them repeatedly, he will eventually hold them, so that he can blast them with a sonic wave, hit them with a whirlwind punch or throw them backwards. All of these throwing effects depend on the direction the d-pad is being pressed when pressing the punch button. His most powerful attack is his D. Punch, which must be charged with a certain button, which can be discharged. The D. Punch is also a limited attack.
The bonus levels are an adaptation of the arcade version. The major difference is that since there is no punch pad, the player must charge strength by repeatedly rotating the d-pad.
Like with most beat 'em-ups of the era, the Japanese version had female enemies which were replaced by male ones in the American and European versions, mostly because of Nintendo of America's strict censorship issues at the time. Only the first two stages of the game feature human enemies.
Source: Wikipedia, "Sonic Blast Man", available under the CC-BY-SA License.