Translation:She is executing him.
-taH means the execution is ongoing. She executed him means the execution is completed. Being ongoing and being completed are mutually exclusive states.
In Klingon, there are four mutually-exclusive "type 7" verb suffixes: -taH continuous, -lI' progress, -pu' perfective, and -ta' accomplished. -taH and -lI' both indicate that the verb is ongoing; -lI' has the further meaning that progress is being made toward a known stopping point. -pu' and -ta' both indicate the action is completed; -ta' has the further meaning that the action was undertaken deliberately. One can always choose to use -taH even if progress is being made toward a known goal, and -pu' may always be used for a completed action even if the action was undertaken deliberately. A verb that lacks any type 7 suffix is not continuous and not perfective; if the meaning is meant to be there, the suffix is not optional.
The use of these suffixes doesn't include information about when the action happens, only how it unfolds over time. muHtaH could be used to refer to an ongoing execution in the past, an ongoing execution happening right now, or an ongoing execution to occur in the future. muHpu' could be used to refer to an execution that was completed in the past or one that will be completed in the future. (It's unlikely that an execution that is occurring right now would be described as completed.)
qama' muH 'avwI' the guard executes the prisoner
The action is not described as ongoing or completed. It might occur in the past, present, or future, but it's being described as happening in the moment.
qama' muHtaH 'avwI' the guard is executing the prisoner
The action is ongoing. It might be a past action that was ongoing, or action that is currently ongoing, or an action that will happen in the future and will be ongoing.
qama' muHlI' 'avwI' the guard is executing the prisoner
Same as muHtaH, only it implies that the act of executing was/is/will be proceeding toward a known stopping point (very probably the death of the prisoner).
qama' muHpu' 'avwI' the guard executed the prisoner, the guard has executed the prisoner
At whatever time the sentence is placing your viewpoint, the execution is completed. If the execution happened yesterday, then it was completed yesterday. If the execution is going to happen tomorrow, then you're talking about a time after the future execution is finished.
qama' muHta' 'avwI' the guard executed the prisoner, the guard has executed the prisoner
Same as muHpu', except you're making the point that the guard deliberately undertook the execution.
The past translation that seems closest to me would be, "She was executing him." Since the complex tenses in English and the aspect markers in Klingon are not perfect matches for each other, there could be other ways to translate this depending on context. Due to the way this courses is presented in Duolingo, we ask that you always use the English ending "-ing" when you see the Klingon verb suffix -taH.
I was about to ask a question, but then I looked up the pronoun prefix chart, and answered it myself. But if anyone is wondering: expressing "he/she/it....he/she/it" does not require a pronoun prefix. So muHtaH can mean "is executing" or "he/she/it executes him/her/it".