We report the first observations, to our knowledge, of nonlinear optical effects in large (millimeter-sized) droplets. Stimulated Raman scattering (SRS) and laser-induced breakdown (LIB) are simultaneously observed in acoustically levitated millimeter-sized glycerol droplets irradiated by either a frequency-doubled (532-nm) or a frequency-tripled (355-nm) Nd:YAG laser. The two processes, which occur above a nearly coincident irradiation threshold, are conjectured to arise from a common initiation mechanism: self-focusing. LIB generates vapor bubbles within the droplet, resulting in the quenching of SRS emission.