'The Bomber' topped Sky Sports' opening bill of the new season, and produced a measured, disciplined performance against an experienced opponent.
Miranda provided a threat early on, applying pressure in short bursts in an attempt to put rounds in the bank.
Round seven was the breakthrough for Bellew, who looked to have Miranda hurt but backed off to line up a late burst.
Bellew finished the job in round nine, landing a huge body shot which forced the Colombian to drop to one knee and tell the referee he did not want to continue.
The Liverpudlian improves his record to 18-1 as he continues to search for a world-title opportunity.