John Gill Commentary Mark 1:34

"And he healed many that were sick with divers diseases, and cast out many demons; and he suffered not the demons to speak, because they knew him." — Mark 1:34 (ASV)

And he healed many that were sick of divers diseases
Not that there were some, who had some sorts of diseases, whom he did not heal; but he healed all that came, or were brought to him, which were many, of every sort of disease, which were divers, with which they were afflicted:

and cast many devils ;
even as many as were brought to him, or were possessed with any:

and he suffered not the devils to speak ;
either for him, or against him; which shows his great power over them:

because they knew him ,
or "that they knew him": He would not suffer them to say a word about him, because he knew that they knew that he was the Christ, the Son of God, or he would not permit them to say who he was.

This was because he had others to bear witness of him, and better testimonies than theirs, and lest his enemies should reproach him with an agreement and familiarity with them.