The triaxial deformation in Be-10 is investigated using a microscopic alpha+alpha+n+n model. The states of two valence neutrons are classified based on the molecular-orbit (MO) model, and the pi-orbit is introduced about the axis connecting the two alpha-clusters for the description of the rotational bands. There appear two rotational bands comprised mainly of K-pi = 0(+) and K-pi = 2(+), respectively, at low excitation energy, where the two valence neutrons occupy K-pi = 3/2(-) or K-pi = 1/2(-) orbits. The triaxiality and the K-mixing are discussed in connection to the molecular structure, particularly, to the spin-orbit splitting. The extent of the triaxial deformation is evaluated in terms of the electro-magnetic transition matrix elements (Davydov-Filippov model). The obtained values turned out to be gamma = 15 degrees similar to 20 degrees. Furthermore, the mirror symmetry breaking of the triaxial deformation of C-10 is investigated. The triaxiality of protons in C-10 is much larger than that of neutrons in Be-10 due to the weak binding nature of the valence particles. This agrees with the recent experiment which suggests the mirror symmetry breaking of these nuclei through the beta-decay transition strength.