This question is answered fairly simply in the film. Immediately after the opening credits, we read the following introductory text:
Early in the 21st Century, THE TYRELL CORPORATION advanced robot evolution into the NEXUS phase - a being virtually identical to a human - known as a Replicant.
The NEXUS 6 Replicants were superior in strength and agility, and at least equal in intelligence, to the genetic engineers who created them.
Replicants were used Off-World as slave labor, in the hazardous exploration and colonization of other planets.
After a bloody mutiny by a NEXUS 6 combat team in an Off-world colony, Replicants were declared illegal on earth - under penalty of death.
Special police squads - BLADE RUNNER UNITS - had orders to shoot to kill, upon detection, any trespassing Replicant
This was not called execution.
It was called retirement.
We don't have any more information on the exact reasons Replicants were declared illegal on Earth. We might guess that it was either a retaliatory, collective punishment, or perhaps a genuine safety precaution.
So, these orders and the law they were based on are the reason for the Blade Runners' actions, in general.
Later in the film, when asked about his feelings towards the Tyrell Corporation, Deckard explains his own, unemotional take on the situation:
Replicants are like any other machine. They're either a benefit or a hazard. If they're a benefit, it's not my problem.
Apparently, if we're to take him at his word, Deckard feels that the Replicants he has retired were posing a hazard, rather than providing a benefit.