Abstract The development of soft robots for deep-ocean exploration presents significant challenges, particularly in advancing actuation technologies. There is a growing need to integrate unconventional actuation methods into bio-robotic designs to enhance configurability, adaptability, and safe interaction with humans and the environment. These novel actuation approaches, which closely mimic the function of natural muscles, address key trade-offs in soft robotics design and improve performance in underwater exploration. In this study, we present the design, fabrication, and evaluation of a fully soft jet propulsion unit actuated by coiled NiTi shape memory alloys (SMA) activated through Joule heating. The propulsion system, constructed from platinum-cured silicone, is designed to replicate the biological locomotion of cephalopod species. We investigate the effects of key design parameters, including the location and number of embedded SMA actuators, input power, and actuation frequency, on the swimming performance of the soft robotic system. Experimental results demonstrate that the jet propulsion unit achieves forward locomotion at a rate of 14 cm per pulse, corresponding to 3.2 cm/s (0.22 body lengths per second). Additionally, we explore the scalability of the system for practical deployment in confined spaces by introducing a 4 cm-long mini jet, which achieves an average swimming speed of 5.5 cm/s (1.37 body lengths per second). This work contributes to the advancement of soft robotic technologies for underwater exploration by providing insights into the development of bioinspired jet propulsion mechanisms.