One way of solving this issue is to encourage/mandate the concerned agencies to go in for proper covers for covering these mounds of mud in all the digging areas till the work is over. Alternatively, they should be transported to far away isolated places where they can be filled as land fill.
Concerned agencies can do well do debate the above issue to arrive at the best of the solutions to ensure that in future digging goes on need based and at the same time the dug out muds are properly taken care of to ensure that they do not result in any safety hazard including raising air pollution in those areas.
A proper cover used for all mounds of mud would solve the issue of air contamination to a great extent in all such areas. Some countries use special vehicles which can suck all the muds in the around the streets to keep them neat and clean - through debates such vehicles can be introduced in India for different agencies to use them extensively for reducing the content of muds and the like in many streets and roads in different parts of the country.