Benzoxazine is a newly developed thermoset resin that has attracted significant academic and industrial interest due to its excellent properties. However, improving its dielectric performance while maintaining high heat resistant is crucial for expanding its application in 5G electronics. In this study, we designed and synthesized a novel benzoxazine monomer, DFDA-PTB, using p-tert-butylphenol (PTB) as the phenol source and furfuryl diamine (DFDA), derived from furfuryl amine, as the amine source. Two additional benzoxazines with similar structures were also synthesized for comparison. The cured product, poly(DFDA-PTB), was then analyzed to explore the relationship between its structure and properties. The results indicate that the introduction of a furan ring structure enhances thermal stability and reduces the dielectric constant. Additionally, the inclusion of tert-butyl groups further lowers the dielectric constant and dielectric loss. Simulation methods were employed to study the mechanisms behind these improvements. Poly(DFDA-PTB) demonstrated superior dielectric properties, with a dielectric constant of 2.51 and a dielectric loss of 0.0018 at 10 GHz. It also exhibited excellent heat resistance, with a char yield of 45.4% at 800 °C. These properties make poly(DFDA-PTB) a promising candidate for electronic packaging and communication applications.