The evolution of the structural and transport properties of the Tl2Mn2O7 pyrochlore and three derivatives obtained by chemical doping at the Tl and Mn sublattices have been studied under high pressure conditions up to 9 GPa. Depending on the relative compressibilities of Tl-O versus Mn-O chemical bonds in Tl2Mn2O7, Tl1.8Bi0.2Mn2O7, Tl1.8Cd0.2Mn2O7, and Tl2Mn1.8Sb0.2O7 pyrochlores, a different pressure evolution of the Mn-O bond lengths and Mn-O-Mn angles, governing the magnetic superexchange, has been observed. The transport properties under pressure are also strongly affected by the electronic doping introduced by the chemical substitutions; the formation of frustrated spin systems is observed at high pressures for the Bi- and Cd doped samples, being responsible for a dramatic increase in resistivity. As magnetism and transport are strongly correlated in this system, the variations of the Curie temperature, associated with characteristic metal-to-insulator transitions, are interpreted as a function of the structural changes and the charge carriers density, which varies by orders of magnitude from electron-doped (with Sb) to hole-doped (with Bi, Cd) materials.