We show that an individual droplet of liquid metal can be a source of coherent terahertz radiation when it is excited by two femtosecond laser pulses of the same frequency. Under certain delays between these pulses, the intensity of terahertz radiation increases by more than 3 orders of magnitude. We describe the experimental results with the model of dynamic gain control, which considers the interaction of both laser pulses with the droplet and explains the terahertz-generation process by taking into account the dynamics of electrons and ions after photoionization of the metal droplet. The spatial distribution of terahertz radiation has a forward-directed contribution, whose polarization properties are well described by a nonlinear susceptibility of the second order. Our theoretical estimations based on the experimental data show that under the dynamic gain control the observed terahertz output can be considerably increased. Joint generation of X-ray, ultraviolet, and, as shown in the present work, terahertz radiation allows one to forecast that a free-falling photoexcited droplet of liquid metal is a promising source of multifrequency electromagnetic radiation for extreme nonlinear laser science.