A novel microwave and millimeter wave signal generation system is proposed and numerically demonstrated using an optically pumped quantum dot (QD) spin-polarized vertical-cavity surface-emitting laser (spin-VCSEL) with optical injection. Different from previous optical injection systems, the signal frequency in our proposed system is dominated by both the birefringence-splitting and injection detuning frequencies. By flexibly tailoring the frequency detuning and birefringence rate, the frequency ranges from a few gigahertz to nearly 150 GHz can be obtained. To evaluate the signal quality, the dynamical behaviors of the proposed system and the characteristics of the generated millimeter wave signal are evaluated including the center frequency, power, linewidth, and phase variance. We further adopt the optical feedback structure to improve the microwave and millimeter wave signal performance. Results show that the signal linewidth and phase variance can be optimized by three to four orders of magnitude. Compared to the case of a solitary QD spin-VCSEL, this work shows more stable performance, particularly in the frequency range above 90 GHz. This scheme offers an approach for high-purity microwave and millimeter sources in wireless communication and radar systems.