Seems pretty simple.
However, even a seemingly straightforward teaching, can be understood in different ways by different people at times. This mishnah has featured in Chasidic-Misnagdic debate over the years.
Exhibit one -
Chasidim who davened late were criticized for missing zeman tefillah. One answer given by R. Yitzchak Meir of Gora Kalwaria was as follows. The mishnah says aveirah goreres aveirah. However, according to the Chasidic respondent, those Chasidim who davened late, after davening would learn Torah. If so, according to him, that proves that their davening late was not an aveirah, but rather a mitzvah, since it was followed by another mitzvah, rather than by an aveirah (source)
Misnagdic responses to this clever defense could be as follows.
1) Mitzvah goreres mitzvah doesn't mean that one mitzvah observance will, with total certainty, follow another (and conversely with aveiros). Rather, it means that it will bring another mitzvah opportunity in its wake, following it. A type of positive spiritual momentum, if you may. In the final analysis, however, the person involved will have to choose if they will continue in the mitzvah path or not, by acting to take advantage of the new opportunity, or to lose the momentum, and squander the new opportunity.
Therefore the fact that people were learning after davening late, doesn't prove that the davening late was entirely proper. It may be that they just took separate action to move on to learning, not that they coasted there with the momentum of what they did previously.
2) Davening late (at least within some type of correct time frame, e.g. not davening shacharis during the time of mincha) is not an aveira (such as eating non-kosher or wearing shatnez), but rather carrying out a spiritual activity without following its prescribed regulations. Such a act might be endowed with different dynamics than an actual full-fledged aveirah.
3) There may have been another, possibly unseen, or unnoticed, act between davening late and the learning, which arrested the initial negative spiritual momentum.
Exhibit two -
Rebbe Yitzchak of Radvil asked as follows. We put tefillin on in the morning. This should lead to more mitzvos, because מצוה גוררת מצוה. So everyone should be a tzaddik, as this mitzvah should lead to another, which would lead to another, and on, and on. Why don’t we see this happening? He answers; it depends on how the person does the mitzvah. If he does it with joy, then definitely so. If not, however, it won't have this ability (source, p.8-9).
A Misnagdic response to the above would be (IMHO) that, as above in exhibit one, מצוה גוררת מצוה is not an unstoppable force. Rather it is a type of momentum, spiritual momentum. Just as physical momentum has limits, so too does spiritual momentum. Momentum is not inevitability. We would not agree that 'a mitzvah done without simcha' (as if such could be so easily measured or determined, if it exists at all), or otherwise in less than optimal fashion, is devoid of the power of momentum. Misnagdim have a more expansive, inclusive view of spiritual momentum, and don't limit it to what people consider mitzvos done besimcha.
A Misnagdic response to the above would be (IMHO) that, as above in exhibit one, מצוה גוררת מצוה is not an unstoppable force. Rather it is a type of momentum, spiritual momentum. Just as physical momentum has limits, so too does spiritual momentum. Momentum is not inevitability. We would not agree that 'a mitzvah done without simcha' (as if such could be so easily measured or determined, if it exists at all), or otherwise in less than optimal fashion, is devoid of the power of momentum. Misnagdim have a more expansive, inclusive view of spiritual momentum, and don't limit it to what people consider mitzvos done besimcha.
Exhibit three -
A fine contemporary hit song, known as שכר מצוה, states העושה מצוה אחת קטנה בשמחה מגלגלין לו לעשות מצוה גדולה מהראשונה - someone who does a small mitzvah with simcha, the opportunity is given to him to do a greater mitzvah.
While some people may not notice or pay heed, those lyrics actually differ from the mishna in פרקי אבות. While the mishna speaks of mitzvos generally, without classifying them as being smaller or larger, and without discussing if the mitzvah was done besimcha or not, the song lyrics introduce those new classifications/qualifications/limitations. I don't know where the lyrics are from, but I suspect that they are from (a) Chasidic source(s). If someone can shed light on the matter, please enlighten us (note - I subsequently was informed that the source is the תפארת ישראל on the mishnah, עיין שם).
Let us hope that we seize our moments for good, and maintain positive momentum forward.