Several options - release the fretting finger, but only enough to stop the string vibrating - not off completely. Touch the string with another finger from the fretting hand. Touch the string with a finger or palm of the picking hand.Play the next note on the same string, so the original has to stop.After playing the note (with a pick), put the pick back touching the string.
Tapping the string is not going to work - it'll probably make a different sound. Picking gently will make a held note last less time, but not what you want.
Of course, a 1/32 note will vary in length as to the tempo of the song.