Manipulation of Rashba effects in two-dimensional (2D) electron systems is highly desirable for controllable applications in spintronics and optoelectronics. Here, by combining first-principles investigation and model analysis, we use uniaxial stress to control BiTeI monolayer as a Rashba 2D semiconductor for useful spin and transport properties. We find that the stress-driven electron system can be described by an effective anisotropic Rashba model including all the three Pauli matrixes, and uniaxial stress allows an out-of-plane spin component. When appropriate electron carriers are introduced into the monolayer, an in-plane electric field can induce a charge current and three spin current components (including that based on the out-of-plane spin) because of the reduced symmetry. Therefore, uniaxial stress can be used to control such Rashba 2D electron systems as the BiTeI monolayer for seeking promising devices.