Roper's Mill was actually the May Mill, in Foundry Lane, Highfield, Wigan - about a mile from Newtown.
The proprietor Joseph Roper (c.1810 - 1896) was something of an entrepreneur, being a brass founder, farmer, and mine and brick works owner, at different times.
There were two 'Roper's Mills' mills on the May Mill site - the first burnt down as you know, the second was demolished in the 1980s.
At some stage Roper became bankrupt, but was allowed to stay on as the mill manager.
There were however, a number of cotton mills in this district, so it is possible your ancestors worked at a different one.
https://www.wiganbuildings.co.uk/building.php?id=1123