Designing novel two-dimensional (2D) materials is highly desirable for material innovation. Here, we propose monolayered calcium triarsenide (1L CaAs3) as a new 2D semiconductor with a series of encouraging functionalities. In contrast to the ∼33 meV small band gap in bulk CaAs3, 1L CaAs3 possesses a large direct band gap of 0.92 eV with a high hole mobility of ∼104 cm2 V-1 s-1. The electronic properties of 2D CaAs3 can be manipulated significantly by the layer thickness and external strains. Remarkably, 2D CaAs3 suggests a topologically nontrivial-trivial state transition under thickness reduction and strain engineering, which is attributed to the drastic surface relaxation and pinch effect under compression. A semiconductor-semimetal transition is also revealed when the layer thickness is greater than 3L. Furthermore, 1L CaAs3 exhibits prominent visible-light absorption compared with the crystalline silicon. All these desired properties render 2D CaAs3 a promising candidate for use in electronic and photovoltaic devices.