Here is what I found!
The predecessor of the Coast Guard -- the Revenue Marine and the Revenue Cutter Service, as it was known variously throughout the late 18th and the 19th centuries -- referred to its ships as cutters. The term is English in origin and refers to a specific type of vessel, namely, "a small, decked ship with one mast and bowsprit, with a gaff mainsail on a boom, a square yard and topsail, and two jibs or a jib and a staysail." (Peter Kemp, editor, The Oxford Companion to Ships & the Sea; London: Oxford University Press, 1976; pp. 221-222.) By general usage, that term came to define any vessel of Great Britain's Royal Customs Service and the term was adopted by the US Treasury Department at the creation of what would become the Revenue Marine. Since that time, no matter what the vessel type, the service has referred to its largest vessels as cutters (today a cutter is any Coast Guard vessel over 65-feet in length).
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