Bellew made a slow start and appeared to waste an chance to see off his rival before he stepped up his workrate in the ninth stanza.
The 29-year-old Englishman landed a left hook to Miranda’s body and the South American dropped to one knee before informing referee Ian John-Lewis that he did not want to continue.
The win represents Bellew’s 18th in 19 fights, though he looked cautious in the early rounds against an opponent who had fought impressive names in Andre Ward and Lucian Bute.
Bellew had Miranda in trouble on more than one occasion before the finish. At one point the Colombian cleverly played possum, leaning back against the ropes, but Bellew didn’t take the bait and walked to the opposite side of the ring, much to the surprise of the crowd.
Bellew said he had too much respect for his opponent’s power to take a gamble.
“I couldn’t give him the opportunity because he’s a puncher and I’ve wised up as a fighter,” Bellew said.