The chà reading came in with Buddhist scripture as a sound-borrowing from Sanskrit. It gives 古刹 (ancient temple) and the time word 刹那 (a split second), originally the smallest unit of time in Buddhist cosmology.
刂 on the right is the side form of 刀, the indexing radical. It groups 刹 with 切 to cut and 划 to slash; the blade reinforces the image of motion sliced clean to a halt.
杀 on the left supplies the shā sound and a violent edge. In the brake sense the violence is figurative: slamming a vehicle to a hard stop is treated as 'killing' its motion. It also serves as a strong intensifier in casual speech.
