They sound aggressive and come off as blunt.
In today's society, rejecting an apology is never so direct. Assuming one simply wishes to accept their apology without forgiving them, one often would simply continue to explain their side without apologising or forgiving at all. Example:
Adam: "I'm sorry, John. I shouldn't have stolen your car and crashed it into a building."
John: "Adam, that car meant everything to me. Neither of us can pay for the repairs. I just can't forgive you."
Notice that John never verbally forgives Adam, and the fact that he doesn't establishes how upset John is. John wisely avoids an accusatory tone ('you did this and that and that's bad'), but he keeps a hard line and reminds Adam of the grave nature of his offense. Adam knows that an apology is not going to be enough.
If John instead had answered,
"I do not accept your apology" or "How would your apology benefit me?" or "How do you expect your apology to benefit me?"
Adam might have been rightfully upset at John for his nonconciliatory tone. Adam is making an effort to bridge the divide with an apology, and if John attacks that bridge, then he's violated basic etiquette. John needs to at least acknowledge that Adam is attempting to right the wrong, however insignificant that apology may be. If John doesn't others will see him as the unreasonable one.
Personally, I would almost always simply accept the apology, unless I've been very seriously wronged.
"Rejecting an apology" is very difficult to do tactfully, and one of the best ways to do this is to let them know that they have not done enough; ask them to do something to make it up to you. For example, John might say,
"Thank you for apologising, Adam. Would it be possible for me to use your car to get around while I try to get the money to repair mine?"
This way, you attempt to solve the original problem, and the other person feels strongly obligated to comply (don't abuse this by asking for unreasonable things, though). Often, close friends will (somewhat humorously) ask the other to buy them a drink for minor transgressions.