If the driver applies brakes, the vehicle will accelerate and ultimately stop. However, the distance that it travels before stopping (even after the application of the brakes) is known as the stopping distance. Thus, higher the travel speed, more will be the stopping distance. If the vehicle is at running at 40 miles per hour, it will require more distance and time to stop than if it was running at 30 miles per hour. Hence, at the point of impact, car that was traveling at 40 miles per hour will have a higher speed and consequently a higher momentum (at the point of collision), as compared to the scenario when the car was running at 30 miles per hour. A higher momentum will impact the deer more severely as compared to a lower momentum, thus, injuring it more severely.
Hope this helps.