According to Nichiren, there are two ways to look at your karma.
There is no avoiding karmic retribution. All karma bears fruit - whether good, bad or neutral. I guess there are ways to delay or avoid karmic retribution temporarily, but it is impossible to permanently avoid.
Daimoku does not "purify" karma per se. Daimoku is karmic endeavor that can overwhelm bad karma - like ripples in the water become negligible disturbances in the wake of a steaming ocean liner.
According to Nichiren, the proper practice of Daimoku should draw all bad karma immediately to fruition - so that you can deal with it once and for all in this life and be done with it. He compared it to a sharecropper who's debts are deferred from year to year, but the moment the sharecropper seeks to leave, the debt collectors all immediately come to demand payment. All the latent or subtly manifesting karma immediately is called forward and worked through.
Alternatively, from the perspective of the Essential Teaching, the hardships one faces when properly practicing Daimoku is not karmic retribution, but the arising Three Obstacles and Four Devils - the inertia and opposition that arise to hinder our practice. Overcoming these hindrances is then an opportunity to demonstrate the efficacy of practice, while also being a personal realization of the fruits of practice.
As Nichiren counseled Shijo Kingo when he was suffering through persecution by his lord and fellow samurai who wanted to kill him -
Drink sake only at home with your wife, and chant Nam-myoho-renge-kyo. Suffer what there is to suffer, enjoy what there is to enjoy. Regard both suffering and joy as facts of life, and continue chanting Nam-myoho-renge-kyo, no matter what happens. How could this be anything other than the boundless joy of the Law? Strengthen your power of faith more than ever.
I've been thinking about these two ways to view karma and it occurred to me it was useful as a lens to consider differences between the Gradual Path and the Sudden Path, the First Three Teachings and the Perfect Teaching.
First the terminology - Gradual and Sudden people with a zen background may be familiar with, although what we mean here may be different.
The Gradual Path is one which we progress to Arhatship or Buddhahood, as the case may be, gradually over the course of kalpas. If we enter the path of the Arhat, we follow the teaching of the Four Noble Truths and Eight Fold Path until we exhaust our karma until we attain Nirvana and finally the Parinirvana. In the various Mahayana Bodhisattva paths, we may similarly pursue Buddhahood/Arhatship, or we may pursue some greater vision of Buddhahood through practice of the 6 perfections (paramitas). The point is that all these paths are gradual involving a linear progression toward the goal.
In the Sudden Path, the moment one opens themselves to Buddhahood (adhimukti), they are instantaneously transformed and enter the Buddha path. Practice is no longer a progression toward Buddhahood, but an instantaneous transformation into Buddhahood. If you want to be a Buddha, be a Buddha. As the Lotus Sutra counsels, enter the Buddha's room, put on the Buddha's robes and take the Buddha's seat of practice. This is a radical vision which at times has been interpreted into a complacent attitude wherein people believe that anything they do is Buddhahood. This is true to an extent, but it avoids the implications in this interpretation of Buddhahood in which all of the dharma realms, from Avici Hell to the highest grades of Bodhisattvahood are contained in the Mind of the Buddha. I will come back to this.
In terms of the Four Teachings, this is a Tientai means of systematizing the Buddhist canon. The subject is too big to discuss in detail here. In brief, Zhiyi, the founder of Tientai Buddhism, categorized the Buddha's teachings into 4 categories - Tripitaka, Provisional Mahayana, Distinct and Perfect. These categories generally follow the Buddhist tetralemma as applied to the view of dharmas. (there are peculiarities to Zhiyi's ideas which may not correspond to understandings in other forms of Buddhism; that is neither here nor there. To appreciate Zhiyi's broader message and implicit critique of Buddhism, it is necessary to understand Zhiyi on his own terms.)
Dharmas are True (this is Zhiyi's description of Tripitaka teachings which yield an understanding of Anatman based on deconstruction of compounded dharmas into prime dharmas)
Dharmas are not True (Provisional Mahayana - this is a view of reality as primarily marked by Emptiness and corresponds to many interpretations of Madhyamika which privilege Emptiness over the conditioned)
These two views arrive at essentially the same understanding of reality and their ideas of Arhatship/Buddhahood are nearly identical.
Dharmas are both True and Not True (Distinct Teaching - I'm not clear on this, but the Distinct approach may include two different views - in one, Emptiness and Conditioned are like two sides of a coin - they are two exclusive views of the same dharma, like the heads and tails of a coin - only one is visible at a time. An alternative is that both Emptiness and Conditioned are part of an encompassing "tertiary quid". Emptiness and Conditioned are distinct aspects of a third level of Truth - possibly the Emptiness of Emptiness, but I'm not clear on this.)
Dharmas are neither True nor Not True (Perfect Teaching - Emptiness and Conditioned are completely identified such that looking at emptiness reveals the conditioned and looking at the conditiond reveals emptiness; one cannot look at one without out simultaneously seeing the other in the same view. Most of Tientai Buddhism is an exposition of the implications of this view and the means to achieve entry into it. I'll leave it at that.)
Karma in these four teachings takes on different connotations which essentially add up to gradual paths in the first three teachings, and Sudden path in the Perfect teaching, although some Distinct teachings can be sudden also.
All this is to say, nothing changes between the Gradual and Sudden Paths, or the Three Teachings and the Perfect Teaching. The difference is the manner in which we frame karma. In the Gradual paths, karma is a linear progression with a beginning and end. In the Sudden path, karma is instantaneous (instant karma gonna get you); cause and effect are simultaneous, which is to say, the appearance of linearity is an illusion. There is no past, no future, only the present. If that is so, how can we talk about a linear progression in Karma?
When we enter into an instantaneous sense of time, there is only THIS, in which cause and effect are both Now. How can we talk about a future Buddhahood? If there is Buddhahood, it has to be now. What we do is re-envision this moment AS a permutation of Buddhahood.
For a person entering the Buddhapath for the first time, the full implications of this doctrine are probably lost. In a way, this teaching is a cure for people who envision Buddhahood as something OTHER and SEPARATE from NOW, whether its envisioning Buddhahood in a future date in this life, or a future lifetime. Instead, we see this moment not as progression to an attainment, but rather perpetual perfection of what has already been attained.
Anyway, the point is, whether you see life as overcoming "bad" karma, or you see life as the eternal "play" of Buddhahood, its really a matter of what your frame of reference is.