We present an entirely new sample of 388 low-mass galaxies (M_*_<=10^10^M_{sun}_) that have spectroscopic signatures indicating the presence of massive black holes (BHs) in the form of active galactic nuclei (AGNs) or tidal disruption events. Of these, 70 have stellar masses in the dwarf galaxy regime with 10^8^<~M_*_/M_{sun}_<~10^9.5^. We identify the active galaxies by analyzing optical spectra of a parent sample of ~23000 low-mass emission-line galaxies in the Galaxy and Mass Assembly (GAMA) Survey Data Release 4, and employing four different diagnostics based on narrow emission-line ratios and the detection of high-ionization coronal lines. We find that 47 of the 388 low-mass active galaxies exhibit broad H{alpha} in their spectra, corresponding to virial BH masses in the range M_BH_~10^5.0-7.7^M_{sun}_ with a median BH mass of <M_BH_>~10^6.2^M_{sun}_. Our sample extends to higher redshifts (z<=0.3; <z>=0.13) than previous samples of AGNs in low-mass/dwarf galaxies based on Sloan Digital Sky Survey spectroscopy, which can be attributed to the spectroscopic limit of GAMA being ~2mag deeper. Moreover, our multi-diagnostic approach has revealed low-mass active galaxies spanning a wide range of properties, from blue star-forming dwarfs to luminous "miniquasars" powered by low-mass BHs. As such, this work has implications for BH seeding and AGN feedback at low masses.