The effects of Ta substitution on the superconducting and magnetic properties of the $(Ru_{1-x}Ta_x)Sr_2(Gd_{1.4}Ce_{0.6})Cu_2O_z(0{leq}x{leq}0.5)$ system have been investigated. The X-ray diffraction measurements indicate that the Ta ion replaces Ru sites up to x = 0.4. It is found that the Ta substitution for Ru significantly reduces the weak-ferromagnetic component of the field-cooled magnetic susceptibility without an appreciable change of room temperature thermopower at lower Ta doping level below x = 0.2. The resistive transition temperature tends to decrease monotonically from 27 K for the x = 0 sample to 16 K (9 K) for the x = 0.4 (x = 0.5) sample. These results suggest that superconductivity of the $(Ru_{1-x}Ta_x)Sr_2(Gd_{1.4}Ce_{0.6})Cu_2O_z$ compound is not significantly affected by the magnetic state of the Ru sublattice. The experimental results are discussed in connection with previous reports on the effects of Nb substitution.