The movie started in a desert, with a man in agony who's missing his legs (probably ripped by stretching with bikes or cars). A man (the protagonist) comes along and gives him water. They have a little chat, probably asking to be killed, and I'm not sure but I think he does shoot him. I think next scene the protagonist is being chased (Mad Max style) and he is riding a black modified motorcycle that even delivers grenades near the exhaust from a push of a button in the handle.
The movie is Steel Frontier (1995) starring Joe Lara and Brion James.
Mad Max meets the Man With No Name in this futuristic story of a gunfighter (Joe Lara), who goes after a band of marauders who are terrorizing everyone and killing indiscriminately. As with the spaghetti westerns, the lone gunman enters into a town where the people have lost the will to fight back and proceeds to kill off the bad guys single-handedly. But once he is out-numbered totally and wounded, some do find the capability to fight back. Chief of those who try to aid him is a widow (Stacie Foster) with a young son. Brion James plays the general in charge of the marauders.
This could be Warriors of the Wasteland (1983), a movie with people riding around in the badlands on bikes and in bizarrely modified cars. Watching it, it is painfully obvious that it is aping The Road Warrior.
At about 14:00, the hero (played by Giancarlo Prete) strikes up a conversation with a critically injured man, who he eventually agrees to mercy kill.
(The film also features Fred Williamson, who also played a tough guy in another 1983 post-apocalyptic motorcycling motion picture, Warrior of the Lost World.)