In this work, a novel large-orbit electron beam generated by a Cuccia coupler for a Ka-band third-harmonic slotted is proposed. The Cuccia coupler was originally used in the electron coupler for amplitude modulation and power control at ultrahigh frequencies. It is demonstrated by the 3D-PIC simulation that a 6 kV, 0.5 A beam will be gyroresonantly accelerated when a microwave power of 16 kW at 10 GHz is injected into the coupler, from which a 37 kV, 0.5 A large-orbit electron beam will be obtained; it is characterized by a relative velocity spread lower than 1% and a velocity ratio α (υ⊥/υz) up to 2.3. Moreover, other electron beam parameters including transverse velocity (υ⊥), longitudinal velocity (υz) and deviation of guiding center could be adjusted independently, whereas these are rather difficult for the cusp gun. Finally, the Ka-band third-harmonic slotted peniotron in 2π mode driven by such a beam is verified by 3D-PIC simulation, which is predicted to yield an output power of 8 kW at 30 GHz, with a microwave power conversion efficiency up to 50% and a device efficiency up to 43%, respectively.