If you hate the low skilled, then raising the minimum wage is an excellent idea, because it will prevent them from being gainfully employed.
Why not? If Peter's labor is only worth $X but minimum wage is raised to $X+5, a company can reasonably be expected to fire Peter. Now Peter is out of a job. Should I just take it on your word and evaluate policy based on its purported intent and not on the consequences?
You're not evaluating it based on consequences but what you think would be potential consequences.
Instead, run an experiment and see what actually happens. Actually don't, since we already have data that what you describe is not happening.
Further, if a job is sometimes done by people "on the side" who have low income requirements. (Jobs seen as student jobs come to mind.)