One of the predominant techniques used in the area of data mining is association rule mining. In real world, data mining analysts usually are confronted with a dynamic environment; the database would be changed over time, and the analysts may need to set different support constraints to discover real informative rules. Efficiently updating the discovered association rules thus becomes a crucial issue. In this paper, we consider the problem of dynamic mining of association rules with classification ontology and with non-uniform multiple minimum supports constraint. We investigate how to efficiently update the discovered association rules when there is transaction update to the database and the analyst has refined the support constraint. A novel algorithm called DMA_CO is proposed. Experimental results show that our algorithm is 14% to 80% faster than applying generalized associations mining algorithms to the whole updated database.