We present two newly designed two-dimensional (2D) thermoelectric materials ScP and ScAs, which are stretchable up to 14% as well as dynamically and thermally stable up to 700 K. From a systematic study using density-functional calculations, ab initio molecular dynamics simulations and phonon studies, we find that these compounds are narrow band gap semiconductors and crystallize in a puckered structure, as is the case for many experimentally realized 2D materials like phosphorene and arsenene. The transport properties of these compounds are estimated using the semi-classical Boltzmann transport approach. The lattice thermal conductivity (kl) in the unstrained system is estimated to be 8.3 and 5 W m-1 K-1 for ScP and ScAs respectively which are less compared to those of pristine phosphorene (24-110 W m-1 K-1) and arsenene (6-30 W m-1 K-1). Furthermore, the kl of these compounds becomes ultra-low (∼0.45 W m-1 K-1), when they are subjected to optimum tensile strain conditions. Highly dispersed bands of ScP and ScAs, due to strong p-d hybridization, give rise to large electrical conductivity (∼108 S m-1) which is two orders higher than that of arsenene and phosphorene. The strain also brings nearly a two- and three-fold increase in the Seebeck coefficient with respect to the unstrained value in these compounds. Overall, the strain tunable large figure of merit (∼0.65-0.9) makes these compounds promising thermoelectric materials. © 2019 The Royal Society of Chemistry.