The electric circular saw is an important tool for forest sawing operations, and the vibration characteristics of the circular saw directly affects its service life and safe operation. In order to facilitate the installation and disassembly of the circular saw, the circular saw was connected to the tool holder through a clearance fit between the shaft holes. This fit cannot be accurately expressed using simple supported or clamped boundary conditions. Under the framework of the absolute nodal coordinated formula (ANCF) with a follower coordinate system, the high-speed flexible circular saw model was established by using spatial annulus sector elements, and spring constraint elements with radial clearance were introduced to simulate the boundary conditions of clearance fit. Based on the Darrell principle, taking into account the generalized centrifugal and Coriolis forces in rotational motion, the nonlinear dynamic differential equation of the circular saw model was established. By comparing with other references, the validity of the circular saw model was verified. The influences of fit clearance, rotational speed, and geometric shape on the vibration characteristics and critical speed of the circular saw were analyzed.