Self-healing soft robots show enormous potential to recover functional performance after healing the damages. However, healing in these systems is limited by the recontact of the fracture surfaces. This paper presents for the first time a shape memory alloy (SMA) wire-reinforced soft bending actuator made out of a castor oil-based self-healing polymer, with the incorporated ability to recover from large incisions via shape memory assisted healing. The integrated SMA wires serve three major purposes; (i) Large incisions are closed by contraction of the current-activated SMA wires that are integrated into the chamber. These pull the fracture surfaces into contact, enabling the healing. (ii) The heat generated during the activation of the SMA wires is synergistically exploited for accelerating the healing. (iii) Lastly, during pneumatic actuation, the wires constrain radial expansion and one-side longitudinal extension of the soft chamber, effectuating the desired actuator bending motion. This novel approach of healing is studied via mechanical and ultrasound tests on the specimen level, as well as via bending characterization of the pneumatic robot in multiple damage healing cycles. This technology allows soft robots to become more independent in terms of their self-healing capabilities from human intervention.