I totally agree with 2x4strgkramers about the distance between thumb and strings. Keeping your thumb too far away from the strings will not only affect accuracy, but also speed.
Mark King is a very good example.
Look at how his thumb is always really close to the strings. You will also notice that the movement is coming from his wrist and thumb rather than his arm. This allows a powerful, quick and accurate slap without the need for much energy.
What I often do though to mute the E-String is wrap my left-hand thumb around the neck and touch the E-String. This is one common way. Other times, I could use the middle finger if I am not currently fretting with it (
here's a video I did using middle finger muting).
But starting to slap with your hand parallel to the strings is also an important factor. If you're having trouble getting the right position, try experimenting with how your arm rests on the bass.
Peace