For 5G and 6G communications, satellites are drawing great attention for global coverage extension and 3-D mobility enhancement. With advancements of satellite hardware, functional satellites are expected to be applied for 6G Internet of Things (IoT) services. In particular, because IoT service has a relatively low computational burden, it is more feasible for satellite edge computing (SatEC) with limited power, making IoT supportable SatEC one of the economically feasible applications for future satellite networks. In this article, an architecture of IoT supportable SatEC is analyzed, and the corresponding network slice scheduling is proposed. First, a multiobjective optimization problem for IoT supportable SatEC is formulated with respect to latency, computational power, and transmission power attenuation. The problem is solved for the satellite offloading rate and altitude by using a heuristic algorithm in low time complexity with time-varying satellite constellation topology and various service requirements for simulations. Next, to analyze the expandability of the SatEC IoT network, a sliced SatEC IoT scheduling problem is formulated in the normalized weighted sum of latency, computational power, and transmission power attenuation. Scheduling rules are proposed to prioritize various applications with the results of the scheduling problem and with the proper SatEC offloading rates predefined in the Pareto optimality of the satellite edge multiobjective Tabu search (SE-MOTS). Finally, efficient satellite constellations are determined by comparing low-Earth orbit (LEO) and very LEO (VLEO) satellite networks, in terms of proper satellite altitudes and offloading strategies for IoT supportable SatEC. Based on simulation results, a scheduling rule for sliced satellite network and a proper offloading strategy of different slices are proposed, and an appropriate altitude of the satellite network for sliced SatEC is discussed.