The pyrochlore-type solid-solution formation in a Bi1.6Mg0.8-xCuxTa1.6O7.2-Δ system, synthesized for the first time, is observed at x ≤ 0.56. High-temperature X-ray diffraction showed that the pyrochlore phase exists in air up to 1080 °C, where its thermal decomposition leads to the segregation of (Mg,Cu)Ta2O6. The thermal expansion coefficients of the end member, Bi1.6Mg0.24Cu0.56Ta1.6O7.2-Δ, increase from 3.3 × 10-6 °C-1 at room temperature up to 8.7 × 10-6 °C-1 at 930 °C. Rietveld refinement confirmed that the pyrochlore crystal structure is disordered with space group Fd3̅m:2 (Z = 8, no. 227). Doping with copper results in a modest expansion of the cubic unit cell, promotes sintering of the ceramic materials, and induces their red-brown color. X-ray photoelectron spectroscopy demonstrated that the states of Bi(III) and Mg(II) are not affected by doping, and the effective charge of tantalum cations is lower than +5, while the Cu(II) states coexist with Cu(I). The electron spin resonance spectra display a single line with g = 2.2, ascribed to the dipole-broadened Cu2+ signal. The dielectric permittivity of Bi1.6Mg0.8-xCuxTa1.6O7.2-Δ ceramics may achieve up to ∼105, with the dielectric loss tangent varying in the range from 0.2 up to 12. Multiple dielectric relaxations are found at room temperature and above for all samples.