The leper’s washing his clothes, shaving off all his hair, and bathing himself in water signifies that in addition to experiencing Christ’s death, resurrection, and ascension in his union with Christ through His redemption (vv. 5-7), a sinner who is to be cleansed needs to bear the responsibility himself to deal with and cut off all that is of his old living and natural life.
For the significance of washing one’s clothes, shaving off one’s hair, and bathing oneself in water, see note Lev. 13:341, note Lev. 14:91, and note Lev. 15:51a, respectively.