The effect of the presence or absence of a grounded substrate beneath dielectric targets, including cancer cells, during exposure to the cold atmospheric plasma jet is studied in the experiments and in fluid model simulations for the discharge parameters typical for the medical applications. It is shown that the dynamics of streamers generated in each positive cycle of ac voltage depends on the grounded substrate position. The streamers approach the target more often if the grounded substrate is beneath the target, that provides more intensive plasma-target interaction. In this case, the measured spectrum of plasma jet emission near the target demonstrates much higher intensity compared to an electrically isolated target case. The calculated and measured discharge currents with time demonstrate a mismatch of frequencies of the ac voltage and current over the target. The viability of A431 human skin carcinoma and MX7 mouse rhabdomyosarcoma cells treated by cold atmospheric plasma jet with/without the grounded substrate is measured with MTT assay 24 h after. The results show an enhanced suppression of the cell viability when using the grounded substrate for both cell lines. Achieving effective death of tumor cells with a shorter irradiation time can be considered an advantage of using a grounded electrode beneath the bio target.