Minimally invasive surgery is a popular surgical method which allows surgeons to be able to employ small incisions to perform surgical procedures. Electrosurgical tissue joining is one method used in minimally invasive surgery to achieve hemostasis. The two major issues need to be concerned are the quality of the tissue joint and the potential thermal damage to the surrounding tissues. In this study, a new sequential compression concept was introduced. This concept uses a pair of smaller electrodes to sequentially compress and join multiple locations across the tissue to form a joint. Due to the smaller area of the electrode surface, a higher compression level can be achieved with a smaller compressive force. In this study, different joining times including 1.5, 1.6, 1.7, 1.9, 2.1 seconds with a 98% compression ratio were used to join porcine arterial tissue. In each test, three locations were sequentially compressed and joined. The resulting tensile strength, specific strength, energy consumption, and thermal dose from the sequential compression method were compared with those resulting from the nonsequential single compression method. For the 1.9-second joining time, the specific strength is 2.5 times higher than the highest specific strength achieved by the single joining method, meaning that only 40% of energy is needed to achieve an equivalent joint strength. A finite element model was built to estimate the temperature and thermal dose during the sequential joining process and also confirmed that the resulting thermal dose is much lower than the single joining method. The results validated that the sequential compression concept has the potential to minimize the thermal damage during the tissue joining process.