Despite its growing importance as a Cu resource, studies on tennantite bioleaching are highly limited. One of the key challenges in processing such Cu-As sulfides is their refractoriness and the solubilisation of toxic As. The ultimate goal is to achieve selective bioleaching of Cu with simultaneous immobilisation of As in the leach residues. This study investigated the effectiveness of activated carbon (AC)-assisted bioleaching of tennantite concentrate using a mixed culture containing various “strong” and “weak” Fe-oxidising bacteria/archaea plus a S-oxidising bacterium, with particular emphasis on controlling the solution redox potential (Eh). In the initial flask bioleaching tests, a steady increase in Eh (up to 840 mV) was observed, reflecting the activity of “strong” Fe-oxidisers. In this situation, AC dosing effectively suppressed the Eh value and the highest Cu dissolution (70%) was obtained in the AC-0.01% system, while simultaneously immobilising As. In order to maximise Cu dissolution and As immobilisation, it was found preferable to target the Eh range of 650–700 mV during bioleaching. The next bioreactor tests used the mixed culture of the same origin, but had been subcultured a few generations further on tennantite concentrate. The Eh level remained unexpectedly low (~630 mV) for most of the leaching period, regardless of the AC dosage. It was later found that the bioreactor systems were almost exclusively dominated by Sb. thermosulfidooxidans, a “weak” Fe oxidiser with high Cu/As tolerance. In this case, there was no need to artificially suppress the Eh level by AC dosing and Cu leached readily to a final Cu dissolution of ~60% while As dissolution was suppressed to ~15%. Thus, depending on the microbial community that develops at the processing site, Eh control can be achieved either naturally by the activity of “weak” Fe-oxidisers as the predominant survivors under high Cu/As stress, or artificially by the addition of an Eh regulator such as a carbon catalyst.