"I want to say again, my deepest apology. It has saddened and ached my heart," Mitchell said in the brief statement.
China and Taiwan split in 1949 after the Chinese civil war and the communist takeover on the mainland.
Beijing claims the democratically run island is a renegade province that should not have diplomatic ties with other countries.
"I do want to promise though that this incident will not go unnoticed and that a full investigation will in fact have to be done."
The new Queen's Park stadium in St George's, the capital of Grenada, was built to host matches for the cricket world cup in April.
The previous stadium was destroyed by Hurricane Ivan in 2004.
Taiwan has long wooed countries, particularly small island states, to support its desire for recognition and several Caribbean islands have diplomatic relations with Taipei.
In return, Taiwan has become a major supplier of aid.
Mitchell's government, however, broke off relations with Taiwan in 2005 in favour of strengthening relations with China.