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 ...
190b. The perfect participle generally has an active sense, but in verbs otherwise deponent it is often passive: as, mercátus, bought; adeptus, gained (or having gained).
As I read it (with the help of some other paper grammars) this means: “Perfect participles of deponent verbs generally have an active sense. However, there are deponent verbs which follow ...
I can offer an explanation, but I am unsure if the mechanism I propose is the one that produced this use.
If others have better proof, I will be happy to see more answers.
Consider the previous weekend — assuming you are reading this on a weekday.
It is the newest weekend of all the weekends there have been so far.
It is also the last weekend so far.