This was once official policy. During the Eisenhower administration they had, and I kid you not, "Operation Wetback" that did exactly this.
Simply enforce the existing immigration laws and they will self deport themselves in a tidy manner.
Dry up the jobs and they will have to leave the same way they came.
Fixed.
It's also fascinating to read that this program was instituted with the cooperation and at the behest of the Mexican government who actually wanted to stop laborers from leaving to the U.S.