Devadaha Sutta (MN 101) linked to by @Yuttadhamo is the right sutra to consider, that fully covers this topic. As you can see in MN 101, the Jains too held position that "burning" past karma through exertion and austerity can lead to liberation.
As he interrogates Jains, Buddha makes following points:
- Not all pain comes from causes in the past. Some pain obviously comes from fierce striving, fierce exertion performed in the here-and-now. (As my first teacher used to say, sometimes pain comes from dental crowns and not from karma.)
- Unfortunately, we can't really see how much negative karma we have accumulated, and how much karma has been exhausted so far.
- If we saw that, then in theory we could talk about removing karma through exertion, similarly to how surgeon removes a poisoned arrow, producing pain short-term, but stopping it long-term.
- Unfortunately, that is not possible, because:
- Unfruitted karma that is to fruit in one way, cannot be converted to fruit in another way, through striving & exertion.
- Unfruitted karma that is to fruit in the future, cannot be converted to fruit in the present, and vice versa, through striving & exertion.
- Unfruitted karma that is to bring result of one size, cannot be converted to bring result of another size, through striving & exertion.
Instead, according to Buddha's teaching in MN 101, liberation from
dukkha is achieved by "abandoning of unskillful mental qualities and the attainment of skillful mental qualities in the here-&-now".
Specifically, "skillful mental qualities" refer to 1) "exertion of fabrication against a cause of dukkha" which leads to "dispassion due to the fabrication", and to 2) "looking with equanimity at the cause of dukkha", which leads to "dispassion through the development of equanimity". In other words, cessation of
dukkha is attained through 1) deliberate control of one's perspective, and through 2) equanimity that comes from philosophical attitude.
As an example of typical dukkha-pattern, Buddha tells a story of unshared love, with the protagonist suffering from "sorrow, lamentation, pain, distress, & despair" due to being "in love with her, his mind ensnared with fierce desire, fierce passion". The protagonist then wilfully abandons "desire & passion for that woman" (an effort that serves as "exertion of fabrication against a cause of dukkha") and as a result attains dispassion "due to the fabrication".
With all of the above in mind, Buddha still admits to importance of pushing oneself and overcoming one's limits -- to avoid regress due to indulgence -- but only inasmuch as to have "unskillful qualities decline" and "skillful qualities increase":
So he exerts himself with stress & pain, and while he is exerting
himself with stress & pain, unskillful qualities decline in him, &
skillful qualities increase. Then at a later time he would no longer
exert himself with stress & pain. Why is that? Because he has attained
the goal for which he was exerting himself with stress & pain.
As a result,
A monk, when not loaded down, does not load himself down with pain,
nor does he reject pleasure that accords with the Dhamma, although he
is not fixated on that pleasure.