We present vibrational techniques to pump, mix, and separate dry granular materials using multifrequency vibrations applied to a solid substrate with a standard audio system. The direction and velocity of the granular flow are tuned by modulating the sign and amplitude, respectively, of the vibratory waveform, with typical pumping velocities of centimeters per second. Different granular materials are mixed by combining them at Y-shaped junctions, and mixtures of granules with different friction coefficients are separated along straight channels by judicious choice of the vibratory waveform. We demonstrate that the observed velocities accord with a theory valid for sufficiently large or fast vibrations, and we discuss the implications for using vibrational manipulation in conjunction with established microfluidic technologies to combine liquid and dry solid handling operations at sub-millimeter length scales.