By means of extensive ab initio calculations, a new two-dimensional (2D) atomic material tin selenide monolayer (coined as tinselenidene) is predicted to be a semiconductor with an indirect gap (~1.45 eV) and a high hole mobility (of order 10000 cm(2)V(-1)S(-1)), and will bear an indirect-direct gap transition under a rather low strain (<0.5 GPa). Tinselenidene has a very small Young's modulus (20-40 GPa) and an ultralow lattice thermal conductivity (<3 Wm(-1)K(-1) at 300 K), making it probably the most flexible and most heat-insulating material in known 2D atomic materials. In addition, tinseleniden has a large negative Poisson's ratio of -0.17, thus could act as a 2D auxetic material. With these intriguing properties, tinselenidene could have wide potential applications in thermoelectrics, nanomechanics and optoelectronics.