1. You can mute the low strings with your thumb on the fretting hand.
2. If your playing a fretted note, lets say the 5th fret 2nd string, then you can just lift the finger fretting to stop the ring after its time is up. If that doesn’t work then instead of entirely lifting it then just lift it enough to take of the pressure and that will completely mute it.
3. Or if your playing finger style you can just rest the finger on the string ringing after its time is up.
4. It might also be helpful to use your index finger on your fretting hand as a mute. Just place it over all the strings being played lightly and use the other finger for the notes you want to ring.
These techniques help me out along with many others but trying to explain them would probably be a disaster.