During a heist at the Bobcat Security bank, he was one of the first responders against Trevor Philips, the then-Michael Townley, Brad Snider, and the Getaway Driver. While the crew was taking money he sneaks up on Michael, holding him at gunpoint, and threatened to kill him if he didn't surrender. After being advised by Michael to forget what he saw and leave (using a movie quote that years later would be a key element in the main story), Trevor shoots him in the head, killing him instantly.
Chronologically, Jaspers is the first character to be killed on-screen in the HD Universe.
It's absolutely mandatory for the player to kill him, as trying to shoot him somewhere else, even in the hand to drop his pistol, in an attempt to disable him without killing will cause them to fail the mission, stating that M was killed.
If the player waits for a while after the guard holds Michael hostage, Michael will attempt to try and reason with the guard who simply asks for Trevor to lower his weapon, to which Trevor replies "Ain't gonna happen, pal".
The name "Jaspers" is a Persian name, meaning a keeper or protector of treasure. This is possibly an easter egg placed in the game by Rockstar, because Jaspers is protecting the money inside the vault, therefore making him a "protector of treasure".