  We study $\bar B_q\to {{\rm\bf B}\bar{\rm\bf B}}' l \bar\nu$ and $\bar B_q\to
{{\rm\bf B}\bar{\rm\bf B}}' \nu \bar\nu$ decays with all low lying octet and
decuplet baryons using a topological amplitude approach. In tree induced $\bar
B_q\to {{\rm\bf B}\bar{\rm\bf B}}' l \bar\nu$ decay modes, we need 2 tree and 1
annihilation amplitudes in octet-anti-octet decay modes, 1 tree amplitude in
octet-anti-decuplet decay modes, 1 tree amplitude in decuplet-anti-octet decay
modes and 1 tree and 1 annihilation amplitudes in decuplet-anti-decuplet decay
modes. In loop induced $\bar B_q\to {{\rm\bf B}\bar{\rm\bf B}}' \nu \bar\nu$
decay modes, similar numbers of penguin-box and penguin-box-annihilation
amplitudes are needed. Relations on these semileptonic baryonic $B_q$ decay
amplitudes are found. Furthermore, the ratios of loop topological amplitudes
and tree topological amplitudes are fixed by known CKM factors and loop
functions. The observed $B^-\to p\bar p \mu^-\bar\nu$ differential rate
exhibits threshold enhancement, which is expected to hold in all other
semileptonic baryonic modes. The threshold enhancement squeezes the phase space
and leads to very large SU(3) breaking effects in the decay rates. They are
estimated using the measured $B^-\to p\bar p \mu^-\bar\nu$ differential rate
and model calculations. Modes with relatively unsuppressed rates and good
detectability are identified. These modes can be searched experimentally in
near future and the rate estimations can be improved when more modes are
discovered. Ratios of rates of some loop induced $\bar B_q\to {{\rm\bf
B}\bar{\rm\bf B}}' \nu \bar\nu$ decays and tree induced $\bar B_q\to {{\rm\bf
B}\bar{\rm\bf B}}' l \bar\nu$ decays are predicted and can be checked
experimentally. They can be tests of the SM. Some implications on $\bar
B_{q}\to {{\rm\bf B}\bar{\rm\bf B}}' l^+ l^-$ decays are also given.
