Two-dimensional (2D) SnS and SnSe like black phosphorus have recently attracted great attention for their potential applications in next-generation electronics. Here, first-principles calculations are employed to investigate uniaxial strain behaviors and carrier mobilities of these monolayer structures. They are more structurally stable in armchair strain (y axis strain) than in zigzag strain (x axis strain), because zigzag deformation of the latter can be spontaneously transformed into former. Band gaps exhibit abnormal behavior with armchair strain changing from epsilon(y) = -5% to epsilon(y) = 15%, which is elucidated through the orbital hybridization between p states of S or Se atoms and the p states of Sn atoms. Surprisingly, it found that hole mobility is mainly determined by longitudinal acoustic phonon scattering, while electron mobility is mainly dominated by optical phonon scattering. The mobility can be tuned by uniaxial strain. Tensile strain along armchair direction will reduce carrier mobility. At compressive strain of epsilon(y) = -5%, the mobility of SnSe is increased to mu(x)= 1.40 x 10(3) and mu(y) =2.35 x 10(3) cm(2) V-1 s(-1) for electron, and mu(x), = 1.31 x 10(3) and mu(y) = 1.46 x 10(3) cm(2) V-1 s(-1) for hole. Excellent elastic property, moderate band gap and tunable carrier mobility make SnSe promising for application in nanoelectronics and optoelectronics.