the parable of the good samaritan
The parable of the Good Samaritan isn't about "special responsibility to those we have injured". In the parable:
- The "certain man" was injured by robbers (who stripped and beat him)
- The injured man was ignored by a priest and a Levite
- The Samaritan showed compassion and acted as if he had a special responsibility (even though the Samaritan had nothing to do with, wasn't responsible for, causing the man's injury)
- Jesus's message is to do like the Samaritan did
'Mercy' can be defined as compassion or forgiveness shown towards someone whom it is within one's power to punish or harm.
You seem to be interested in the definition of "mercy".
I slightly disagree with your definition above. If you're able to rescue someone from drowning, for example, then that could an act of mercy, but (assuming you weren't the cause of their being in the water) nothing to do with "punishing" or "harming".
You might like Wikipedia's article on Mercy (I went to it to look for the etymology of the word). An interesting part is at the end,
To be mercy, the behavior generally can not be compelled by outside forces. A famous literary example that alludes to the impact of the ethical components of the mercy on the legal aspects is from The Merchant of Venice when Portia asks Shylock to show mercy. He asks, "On what compulsion, must I?" She responds:
The quality of mercy is not strain'd.
It droppeth as the gentle rain from heaven
Upon the place beneath. It is twice blest:
It blesseth him that gives and him that takes.
That almost argues against your definition: because there might be some special obligation towards someone you have injured.
The corresponding traditional Buddhist virtues, by the way, if you want to research them further, might be the Brahmaviharas (including Karuṇā which is 'translated' as compassion), and ahimsa (harmlessness or non-violence, for example mentioned here).
compassion towards someone who you have punished or harmed
There may be something somewhere in Buddhist scripture, that talks about whether and how to behave towards people you have injured.
Although that's your question I'm not immediately inclined to answer it, because the more important message of Buddhism is, "because you have compassion for people, do not cause them injury".
The basic rules of conduct, for example the five precepts, and the ethical conduct portion of the eight-fold way, are to do with not causing injury.
One of the suttas about the five precepts starts with,
There are these five gifts, five great gifts — original, long-standing, traditional, ancient, unadulterated, unadulterated from the beginning — that are not open to suspicion, will never be open to suspicion, and are unfaulted by knowledgeable contemplatives & brahmans. Which five?
There is the case where a disciple of the noble ones, abandoning the taking of life, abstains from taking life. In doing so, he gives freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings. In giving freedom from danger, freedom from animosity, freedom from oppression to limitless numbers of beings, he gains a share in limitless freedom from danger, freedom from animosity, and freedom from oppression. This is the first gift, the first great gift — original, long-standing, traditional, ancient, unadulterated, unadulterated from the beginning — that is not open to suspicion, will never be open to suspicion, and is unfaulted by knowledgeable contemplatives & brahmans...
The practice of Dana (i.e. gift-giving or generosity) is made especially by laypeople towards monks and nuns; and not because those monks and nuns were injured by the laypeople.
Because it seems to me to be the bedrock of intelligent ethics
Some people think that the "golden rule" is the bedrock of intelligent ethics, e.g. "do unto others as you would have others do unto you", also known as "love thy neighbour as thyself".
I think you'll find that in Buddhism too, for example in the Dhammapada,
All tremble at violence; all fear death. Putting oneself in the place of another, one should not kill nor cause another to kill.
All tremble at violence; life is dear to all. Putting oneself in the place of another, one should not kill nor cause another to kill.
One who, while himself seeking happiness, oppresses with violence other beings who also desire happiness, will not attain happiness
One who, while himself seeking happiness, does not oppress with violence other beings who also desire happiness, will find happiness
Speak not harshly to anyone, for those thus spoken to might retort. Indeed, angry speech hurts, and retaliation may overtake you.
Did the Buddha ever teach that we have a special responsibility to those we have injured?
I'm pretty sure he taught that we have some responsibility to not injure people.
I think that the practice of deliberately (intentionally) injuring someone would be likely to have a negative/undesirable karmic consequence.
I'm not sure it's always possible to undo an injury (which is a reason for avoiding causing injury in the first place).
Answers to other topics on this site, for example What do we do when we've broken a precept?, don't seem to focus on restitution or special responsibility towards the injured party.
The practice of the Buddhist "Metta Bhavana" (or "cultivation of loving-kindness") meditation is meant to develop compassion towards all people, both near and far, both more dear and less dear -- and not especially towards "someone you have punished or injured".