Yes, the mass deportation of illegal immigrants is morally acceptable, because they broke laws in coming to the United States without proper papers. There are already procedures in place that will block a deportation if a person fears that they will be hurt when they return to their country, so deporting those who have simply broken laws is acceptable.
I can't think of anything less acceptable besides maybe murdering immigrants. Right now, there's no reason for them not to be here, because the only reason most of them are here is to gain a pathway to citizenship. Rounding them up and sending them off to nowhere won't help. They left because they're people without a country, now. They want to be Americans, let them.