The mishna says that חרש שוטה וקטן and עבד ואשה are both פגיעתן רעה. But, a woman and eved are technically liable for their damage just that they don't have money to pay with. Whereas a deaf, fool and child are not liable for their actions. Therefore, a woman and eved are responsible to pay after their situation changes and they have their own funds. But a deaf, fool and child remain exempt even after the child would turn into an adult. This is apparent from the mishna and even clearer in rashi who seems to explain the contrast that a woman and eved are really chayev just that they have nothing to pay from. The implication of rashi is clearly that a child is not chayev even if he would have what to pay from.
I mentioned earlier in baba kama that the hagahos ashri here understands from rashi 88b where rafram forced rav ashi to pay for burning a shtar b'yalduso, that a child is chayev to pay when he gets older for damages that he did when he was younger. This seems to directly contradict the implication of rashi here that a kattan will always be patur for his actions?
When one damages there are 2 concepts that require him to pay. One is כלפי שמיא where he violated a "prohibition" and must make amends by repaying the damage. The second is the very practical aspect of compensating the person for the loss that he caused. It could be that the mishna is saying that a child is not liable to compensate for the loss that he caused when he is younger, but the concept of the aveira still exists to some degree. Similar to what the Rama writes in Hilchos Shabbos 343 קטן שהכה את אביו או עבר שאר עבירות בקטנותו אע"פ שא"צ תשובה כשיגדל מ"מ טוב לו שיקבל על עצמו איזה דבר לתשובה ולכפרה אע"פ שעבר קודם שנעשה בר עונשין
Just that the hagahos ashri takes the concept of the rama a step further, it is not merely a chumra or l'fnim m'shuras hadin, but rather כלפי שמיא he is chayev to make amends for actions that caused a loss or damage to others. Therefore, in dinei choshen mishpat he is not chayev to repay, as our mishna implies. But in "issur v'heter" he is chayev to repay.