Both Matthew, chapter 20:32-33, and Luke, chapter 18:41 are similar. Mark indicated that Jesus responded to Bartimaeus (καὶ ἀποκριθεὶς αὐτῷ ὁ Ἰησοῦς). He wanted to know what he wished that Jesus could do for him (εἶπεν Τί θέλεις ποιήσω). The blind beggar replied to Jesus (ὁ δὲ τυφλὸς εἶπεν αὐτῷ) by addressing him as Rabbi or master teacher (Ῥαββουνεί). He wanted to see again, to regain his sight (ἵνα ἀναβλέψω). This did not seem that unusual.
This story of the healing of the blind man at Bethsaida was unique to Mark. Then Jesus laid his hands on the blind man’s eyes again (εἶτα πάλιν ἐπέθηκεν τὰς χεῖρας ἐπὶ τοὺς ὀφθαλμοὺς αὐτοῦ). This time the blind man opened his eyes intently (καὶ διέβλεψεν). His sight was fully restored (καὶ ἀπεκατέστη). Now he began to see everything clearly (καὶ ἐνέβλεπεν τηλαυγῶς ἅπαντα). Thus, this second stage of clear vision needed another physical act to complete the healing of this blind man. Perhaps, that is why Matthew and Luke did not include this story in their gospels.
This story of the healing of the blind man at Bethsaida was unique to Mark. This was a little different healing that did not take place immediately. Instead there seemed to be a two-step process. At first, the blind man looked up or recovered his sight (καὶ ἀναβλέψας). He then said (ἔλεγεν) that he could see people (Βλέπω τοὺς ἀνθρώπους). However, they looked like trees that were walking or walking trees (ὅτι ὡς δένδρα ὁρῶ περιπατοῦντας), not humans.
This story of the healing of the blind man at Bethsaida was unique to Mark, who said that Jesus took the blind man by the hand (καὶ ἐπιλαβόμενος τῆς χειρὸς τοῦ τυφλοῦ). He then led him out of the village (ἐξήνεγκεν αὐτὸν ἔξω τῆς κώμης). There he put spit on his eyes (καὶ πτύσας εἰς τὰ ὄμματα αὐτοῦ). He also laid his hands on him (ἐπιθεὶς τὰς χεῖρας αὐτῷ,). He questioned the blind man (ἐπηρώτα αὐτόν) whether he could see anything (Εἴ τι βλέπεις)? Thus, this healing took place with very physical elements, saliva and a hand laying on his eyes.