This paper explores the nonlinear dynamics of mutually coupled spin-torque nano-oscillators and examines the relationship between non-isochronism and the appearance of exceptional points (EPs). We demonstrate that by manipulating the amplitudes of the driving force and the angles of the external bias magnetic field and spin-polarized current, it is possible to observe and fine-tune the position of EPs. Namely, EPs shift most significantly when the azimuth angle of the equilibrium state is approximately 90° and the system’s non-isochronism reaches its peak. The results of this investigation provide valuable insights for enhancing the performance of spintronic devices in applications such as microwave signal generation, spin-based computing, and sensing.