Mark 3:7 begins a new section in the Second Gospel, and 3:7-12 serves as a bridge passage between the controversy stories (2:1-3:6) and this next section of expanded ministry (3:7-6:6).
The last section ended with the official inception of the plot to kill Jesus (3:6), and Mark follows the news of that scheme with character testimony about Jesus. Mark wants us to see what kind of Person they’re trying to kill. Mark also shows us that Jesus is completely undeterred by their plot; His ministry in 3:7-12 looks identical to His ministry in chapters 1-2.
Then Jesus calls the Twelve Apostles, commissioning them to be with Him, to preach, and to cast out demons. An apostle is one who is sent with the authority of the sender. These men are given authority to do the very things that Jesus does. And these men (with the exception of the traitor Judas) would all go on to give their lives in service to their King Jesus and the saints bought by His blood.
Notes and audio can be found here.