Partially biobased thermoplastic vulcanizates (TPV) with novel morphology, superior properties and partial degradability were prepared by dynamic cross-link of saturated poly(lactide) and ethylene-co-vinyl acetate (PLA/EVA) blends using 2,5-dimethyl-2,5-di(tert-butylperoxy)hexane (AD) as a free radical initiator. EVA showed higher reactivity with free radicals in comparison with PLA, leading to much higher gel content of the EVA phase (Gf-EVA) than that of the PLA phase (Gf-PLA). However, the Gf-PLA increased more steeply at AD content larger than 1 wt % where the reaction of EVA approached to a saturation point. The competing reaction changed the viscosity ratio of the two components (ηPLA/ηEVA) that resulted in a novel morphology evolution of the TPV, i.e., from sea–island-type morphology to phase inversion via a dual-continuous network-like transition and finally cocontinuity again with increasing the AD content. The cross-link and phase inversion considerably enhanced the melt viscosity (η*), elasticity (G′) and the solid-like behavior of the PLA/EVA-based TPV. Meanwhile, superior tensile strength (σt = 21 MPa), low tensile set (Ts = 30%), moderate elongation (εb = 200%) and suitable stiffness (E′ = 350 MPa, 25 °C) were successfully achieved by tailoring the cross-link structure and phase morphology. In addition, the TPV are partially degradable in aqueous alkali. A degradation rate of approximately 5 wt % was achieved within 10 weeks at 25 °C and the degradation mechanism was investigated from both molecular and macroscopic levels. Therefore, this work provides a new type of partially biobased and degradable materials for substitution of traditional TPV.