The product of a gamma radiation experiment gone wrong, Dr. Bruce Banner becomes plagued for the rest of his life, holding within him a massive rage monster that becomes unleashed when Banner becomes angry or stressed. In the months before Marvel's Civil War II storyline, Bruce had been experimenting on himself once more, hoping to keep the Hulk at bay for good. However, as a failsafe, he gives Hawkeye two gamma-irradiated, vibranium-tipped arrows, the only weapon that could kill the Hulk, asking him to kill him if he ever turns into the Hulk again, and Clint agrees.
When Civil War II does happen, the young Inhuman Ulysses receives a vision of Bruce Banner losing control to the Hulk and going on a vicious rampage in the future. As a result, he is confronted by almost every major Marvel hero, hoping to prevent the Hulk-Out from happening. The group of heroes are split however, with some not wanting to take in their friend before he's even done anything wrong. Understandably, Banner starts to become confused and agitated, which is when Hawkeye makes good on his word. According to Clint, he saw Banner's eyes flash with green.
Remarkably, there is enough evidence along with Clint's testimony in court to acquit him with no charges for Bruce's murder. However, the concept of life and the permanence of death is one that is extremely loose in the superhero genre. Naturally, after some time es, the Hulk is brought back to life with a new game-changing evolution to his power set. Though Bruce Banner can die, Hulk will always survive, claiming that he would have done it again considering the vision he saw.
While it's cool to see Banner and Banner come to some sort of reconciliation for the equally traumatic event, the Hulk himself is far from satisfied. In Avengers: No Road Home, Hulk expresses his anger at Hawkeye, mad that instead of taking Banner to get mental help, he just went ahead and agreed to Banner's wishes to kill him along with the Hulk himself. He warns Clint that the two of them should never be alone together. Ever. It looks as though the Jade Giant still has some beef with Hawkeye, and it will be interesting to see as time goes on in Marvel Comics if that grudge will ever come to a head.