Yes, a deponent verb can have an accusative object just like non-deponent verbs do.
If I threaten someone with something in Latin, then alicui aliquid minor.
The person (or other entity) being threatened is in dative, but the threat (death, punishment, fine, ...) is in accusative.
Since minari is a deponent verb, the seemingly passive form can be used as if it were active.
In my experience the non-deponent version minare is less common.
Therefore interrogavi supplicium minatus means "I interrogated and threatened with punishment".
The most natural translation of supplicium depends on context.
As a side note, supplicium is also the plural genitive of supplex, but this interpretation makes little sense in this context.