Evidently, through auxin-induced ethylene production or increased sensitivity to ethylene as in the case of abscission. Auxin can act as a herbicide, too. But I have no proofing papers on my mind to support it.
In plants, phytohormones are acting in a competitive manner. Auxin, though produced in the leaves, is mainly responsible for apical shoot growth and root formation, while leaf expansion and growth is maintained through cytokinins. When high levels of auxin is present in plant leaves that negates and inhibits the effects of cytokinins resulting in leaf expansion inhibition. Nevertheless, small amounts of auxins are actually enhancing leaf expansion but above that low level of threshold, it results in inhibition of leaf expansion.
Plant hormone regulation and effects is a very complicated and still not fully understood field, but that is the current simplified theory thus far.
High concentration of auxin above optimal concentration usually inhibits plant growth. This because high auxin concentration stimulates ethylene production, and consequently ethylene inhibits growth.