By means of first-principles calculations, we investigated the geometric structure, dynamic and thermal stabilities, and electronic properties of the two-dimensional (2D) Janus group III chalcogenide monolayer MoTeB2. The MoTeB2 monolayer exhibits a stable sandwiched structure, and its semimetal electronic structure features the perfect electron–hole compensation. The 1:1 electron–hole carrier ratio and high carrier mobility endow the MoTeB2 monolayer with large and nonsaturating magnetoresistance. Its electronic properties are easily adjustable by minute charge doping and small tensile stains; in particular, the switch of carrier polarity and metal–semiconductor phase transformation can be achieved. This study not only leads to the finding of the Janus MoTeB2 monolayer as a promising 2D material with extraordinary magnetoresistance but also provides a general route to adjust the magnetoresistance effect by compressive stain and charge doping.