Inserting a coverslip into half of a Gaussian laser beam at a suitable tilting angle can make the single-mode laser beam become closely spaced dual light spots at the laser focus. In this way, we can reform the conventional single-beam optical tweezers easily and construct a set of dual-mode split-beam optical tweezers, which can be used to manually rotate a trapped and twisted red blood cell around the optical axis. Furthermore, we demonstrate that the split-beam optical tweezers can also stably trap and orient a birefringent polystyrene micro strip particle, which otherwise will self rotate at a varying speed along the structural principal axes, fast spin about the optical axis in a tilting pose, or precess like a gyroscope, in the original linearly polarized single-beam optical tweezers.