A "Cutter" is a highly specialized craft, and I can't imagine there are any equivalent in the US Navy.
I went thru the Wiki List of Coast Guard Cutters:
https://en.wikipedia.org/wiki/List_of_United_States_Coast_Guard_cuttersAnd only found these. Two that were former USN and five on loan from the USN.
179' Patrol Coastal (WPC)
Cyclone class Coastal Patrol Ships on loan from the United States Navy
• USCGC Tempest (WPC-2)
• USCGC Monsoon (WPC-4)
• USCGC Zephyr (WPC-8)
• USCGC Shamal (WPC-13)
• USCGC Tornado (WPC-14)
187' - Auxiliary Tug (WAT)
• USCGC Redwing WAT-48 Former USN Lapwing Class Minesweeper
306' Edsall Class (WDE)
USCGC Finch (WDE-428), a former US Navy Edsall class destroyer escort