The answer to your question can be found in Chapter Eighteen of this great novel. The conflict that the elopement of Harney and Sophia triggered has resulted in an open shoot out between the remnants of the Grangerfords and the Shepherdsons. Huck, trying to hide from the ensuing chaos, has climbed a tree, and is able to watch what happens to Buck beneath him from his vantage point. As a group of the Sheperdsons come looking for them and firing their guns, Buck and a friend jump for the river and try to escape, even though they are injured, by swimming away. Note how Huck describes what happens:
The boys jumped for the river--both of them hurt--and as they swum down the current the men run along the bank shooting at them and singing out, "Kill them, kill them!" It mad eme so sick I most fell out of the tree. I ain't a-going to tell all that happened--it would make me sick again if I was to do that. I wished I hadn't ever come ashore that night to see such things. I ain't ever going to get shut fo them--lots of times I dream about them.
Huck's reluctance to reveal the true nature of what happened, combined with the way in which he comes across Buck's body two paragraphs later, clearly indicates that Buck was shot to death as he tried to swim away from the Shepherdsons, and that his death was gruesome and painful.