Preparation of low dielectric thermosetting resins by green method is a challenging subject. Herein, unique bio-based benzoxazine monomer E-dea was prepared by a solvent-free method using eugenol as phenol source, and then E-dea and bismaleimide (BMI) were copolymerized to prepare poly(E-dea/BMI-0.86) and poly(E-dea/BMI-1). The comprehensive properties including thermal, mechanical and dielectric properties of the copolymers were studied. Notably, poly(E-dea/BMI-0.86) and poly(E-dea/BMI-1) exhibit low dielectric properties with dielectric constants of 2.85 and 2.79 at 1 MHz, respectively. Besides, the glass transition temperature (T_g), the initial thermal decomposition temperature (T_di) and the flexural strength of poly(E-dea/BMI-0.86) and poly(E-dea/BMI-1) are 167 °C and 169 °C, 333 °C and 321 °C and 115 ± 3.5 MPa and 123 ± 4.9 MPa, respectively. The excellent comprehensive performance is attributed to the interaction between flexible and low dielectric decane segments and rigid oxazine and BMI segments.