Christ could have healed the man by the simple touch of His hand, or even with His words. But He probably realized that the man’s faith was weak.
We find that even after Christ had been resurrected, His disciples’ faith was weak. Their human nature required “physical evidence” of the miracle that had taken place (even above and beyond Christ’s presence among them). (Read Luke 24:40 and John 20:27-29.)
Christ healed the blind man in a “step-by-step” manner, rather than all at once, in order to increase the man’s faith, before totally healing him.