Some really good suggestions already around building an emotional connection with the character and focusing on the effect the death has on those around them, so this is like an optional thing you can add (not an instead-of):
Unfulfilled potential, or regret.
Some of the saddest deaths in media are the ones where the person wanted to do something, but was never able to fulfill that aim, or could only grasp it briefly, in death. In a lot of cases, this is things like the character who has been antagonistic or even a villain, finally has an epiphany and decides they're going to be a better person.... and dies just as we're shown a glimpse of how great they could have been as a hero rather than an antagonist. Sometimes, it might be somebody who used to be great, fell from grace, and gets one last chance to recapture some of their past glory just as they go.
But the extra gut punch version is that the regrets are normal, everyday regrets. The opening of Up is a great example of a death which, with zero dialogue, manages to be emotionally devastating... because the characters dies without fulfilling her big dreams. Her attempt to have a child resulted in a very everyday tragedy, and then through all sorts of everyday problems, she was never able to go on the big adventure she dreamed of.
The death of Hamilton's son in the musical Hamilton, similarly sets up the young man as this promising, bright, optimistic lad who wants to be like his father, challenges somebody to a duel over the family honour, is told to forfeit, and does as he's told... only to be shot before the count to ten to fire even finishes, mirroring the lost potential of a life snuffed out at nineteen.
It's that sense of "I wish they were still in my life", or "What could they have achieved if they were still here?" factor that can really add an extra twist of the knife.