Spectral characterization of super-Earth atmospheres for planets orbiting in the habitable zone of M dwarf stars is a key focus in exoplanet science. A central challenge is to understand and predict the expected spectral signals of atmospheric biosignatures (species associated with life). Our work applies a global-mean radiative-convective-photochemical column model assuming a planet with an Earth-like biomass and planetary development. We investigated planets with gravities of 1g and 3g and a surface pressure of 1 bar around central stars with spectral classes from M0 to M7. The spectral signals of the calculated planetary scenarios have been presented in an earlier work by Rauer and colleagues. The main motivation of the present work is to perform a deeper analysis of the chemical processes in the planetary atmospheres. We apply a diagnostic tool, the Pathway Analysis Program, to explore the photochemical pathways that form and destroy biosignature species. Ozone is a potential biosignature for complex life. An important result of our analysis is a shift in the ozone photochemistry from mainly Chapman production (which dominates in Earth's stratosphere) to smog-dominated ozone production for planets in the habitable zone of cooler (M5–M7)-class dwarf stars. This result is associated with a lower energy flux in the UVB wavelength range from the central star, hence slower planetary atmospheric photolysis of molecular oxygen, which slows the Chapman ozone production. This is important for future atmospheric characterization missions because it provides an indication of different chemical environments that can lead to very different responses of ozone, for example, cosmic rays. Nitrous oxide, a biosignature for simple bacterial life, is favored for low stratospheric UV conditions, that is, on planets orbiting cooler stars. Transport of this species from its surface source to the stratosphere where it is destroyed can also be a key process. Comparing 1g with 3g scenarios, our analysis suggests it is important to include the effects of interactive chemistry.