Depending on the crop you are growing, you may have to chop if it becomes tall and dense enough to start shading your main plants.  Covercrops tend to work best as fertiliser if chopped before becoming too mature as the carbon to nitrogen ratio will be perfect for microbes food at a medium level of maturity.  If growing larger, fast growing annuals you will find that it will naturally die off in the shade of the canopy. Your cover crop is storing valuable nutrients within its biomass and will add these to the soil as a mulch once dead.