We report on a passively mode-locked optically pumped GaSb-based semiconductor disk laser producing stable picosecond optical pulses at a $1.95\mathrm{\mu m}$ wavelength. The gain mirror was comprised of a 15 quantum well InGaSb/GaSb structure. A fast semiconductor saturable absorber mirror with three $\mathrm{InGaSb}/\mathrm{GaSb}$ quantum wells was used to attain self-starting mode-locked operation at a fundamental repetition rate of $881.2\mathrm{MHz}$ . The laser produced pulses with $30\mathrm{pJ}$ energy and a duration of $1.1\mathrm{ps}$ within a factor of 2 of the Fourier limit.