Your mine field idea is more intriguing every day.
So much cheaper and more effective and with modern technology one could imagine mobile "smart" mines, ability to turn off in some circumstances, recognizing livestock or animals versus an illegal, move location, etc. Ultimately the best solution would be real criminal and civil penalties for those who hire, harbor, teach, rent to, etc an illegal. And a legitimate system for legal immigration, even season based or work temporary, that looks for the interests of the country first, which includes demographics, and background checks and tracks the immigrant.