You can mute from both the left hand and the right hand. From the left hand, just lift your fingers off just enough to get a thud sound when you hit the string. If I'm playing across multiple strings, I tend to use the jointed area of my finger to press on/press off.
From the right hand, try not digging into the strings as if you were playing a note, but instead just enough to get that thud out of it as before.
The trick comes from being able to mute within certain parts of a bass line and becoming acquainted with that aspect of coordination.
Fender Jazz Bass Club #31, Connecticut Bass Player #23