We demonstrate what we believe to be a new approach to energetic picosecond 10.2-µm pulse generation based on nonlinear mixing of subnanosecond single-frequency 1338-nm pulses and broadband 1540-nm chirped pulses in a BGGSe crystal followed by a grating compressor for the purpose of seeding high-power CO2 amplifiers. The energy of the 10.2-µm pulses exceeding 60 µJ with 3.4%-rms fluctuation can be routinely obtained. Single-shot pulse duration measurement, performed by Kerr polarization rotation time-resolved by a streak camera, together with the pulse spectrum, indicates the pulse width is between 2.7-3 ps. Numerical calculations show that power broadening and dynamic gain saturation with Rabi-flopping can be induced with such an intense seed in a multi-atmospheric CO2 amplifier. These nonlinear effects greatly suppresses pulse splitting due to the comb-like spectrum of the CO2 molecule. A peak power exceeding 1 TW is expected after multipass of amplification while maintaining an appropriate high intensity by controlling the beam size along the path.