K-shell photodetachment of size-selected B(2)(-) and B(3)(-) cluster anions has been measured and calculated. The experimental absolute photodetachment cross sections exhibit bound resonances below threshold and two shape resonances above the K-shell threshold. Similar results were obtained for all of the cationic products observed, B(+) and B(2)(+) from B(2)(-), as well as B(+), B(2)(+), and B(3)(+) from B(3)(-). The overall agreement between measured and calculated photodetachment cross sections is very good. However, the theoretical study yielded additional bound resonances not observed in the experimental data.