I am going to need to see what these alleged crimes are (and I am not talking about something as "criminal" as being an economic refugee), in addition to credible sources to substantiate the claims. These immigrants are cynically kept under an illegal status so they can be blackmailed into accepting rock bottom wages (try to form a union, complain, etc., and you get deported) for service work that cannot easily be offshored. And unlike Donald Trump, they typically lead productive lives (they actually work for a living instead of getting fat off the labor of others).
The main crime they're committing (besides being here illegally) is fraud. In order to get a job, they either get false documents, or use another person's documents. I know this I because work with dozens of illegals, and a lot of them aren't smart enough to keep it a secret. They also tend to send as much money as they can back to wherever they came from, which hurts the American economy. Of course, the absolute worst thing they do is devaluing American workers. No employer is going to hire an American citizen at a fair wage when there are a dozen Mexicans with fake papers willing to do the job for less.