すてごま literally means a piece used as a sacrifice, and figuratively refers to someone treated as expendable for another person's benefit. In the song, the narrator provocatively asks someone to become his "すてごま" and get caught up in a conflict, making this striking word central to the song's reckless, confrontational attitude.
The narrator of this song wants to be a hero, and he has the gear for it. He has a brand-new tank ("おろしたての戦車で" [in a brand-new tank]), a submarine, torpedoes, fighter jets with the fuel tank always full, and a bomb big enough to burn everything, just waiting for its turn ("爆弾が出番を待ってるぜ" [the bomb is waiting for its moment]). What he lacks is a reason. As he puts it, "何か理由がなければ 正義の味方にゃなれない" [without some reason, I can't be a champion of justice].
So he asks you to provide one. The chorus is a polite request with an ugly core: "君 ちょっと行ってくれないか すてごまになってくれないか" [hey you, would you go for me? would you be my sacrificial pawn?]. A すてごま (捨て駒) is a shogi term for a piece you give up on purpose, and here it means a person thrown away so someone else gets a cause. The ending is blunt: the final chorus swaps "泣いてくれないか" [won't you cry for me] for "死んでくれないか" [won't you die for me], repeated four times. It is a sharp, sarcastic jab at anyone who wants a war and needs someone else's death to justify it.
For learners, notice the soft 〜てくれないか ending ("won't you do this for me?"), which makes every terrible request sound like a casual favour. That politeness is the joke.