Bermuda Settlers of the 17th Century by Julia E. Mercer page 129 Mitchell (From "The Dead Yet Speaking", a family record compiled by Benjamin Gibbs Mitchell born in Warwick Parish, Bermuda, Aug. 5, 1793.Printed for the Author in Baltimore, 1864.)
William Mitchell & Elizabeth his wife came to Bermuda as emigrants about 1619.
Of their children: Elizabeth bapt. 22 Sept. 1619 by Rev. Richard White, first minister in Southampton Tribe who died 1687, very aged.
Daniel Bapt. 2nd Jan. 1622. William bapt. 1625.
One generation appears missing but baptisms of the following children of C. Mitchell, grandchildren of the first William, are recorded in Southampton (Port Royal) tribe:
John born 27th Oct. 1693
William born 7th July 1696
Mary born 6th July 1698
There should be additional information in Hallett's book: Bermuda Early Records (baptism, marriages and burials).
Please contact me directly at email@example.com and I will do my best to find additional info for you.