When does grass stop growing?

it depends. Warm season grasses--Bermuda grass as an example goes dormant and stops growing in the winter months. while cool season grasses (Kentucky blue grass/rye/fescue) go dormant and stop growing in the summer months. Growth may slow at other times of the year, but it does not actually stop unless the lawn/grass is dormant. Dormancy is part of the natural life cycle of grass.