The simple textbook theory says minimum wage laws reduce employment because they make jobs more expensive for employers, and the extra expense either drives some employers out of business, encourages them to produce with less low-wage labor or some combination thereof.
Federal and state minimum wage laws are more complicated than the textbook illustrations because federal and state laws have many exemptions (e.g., tipped employees) and only restrict cash compensation rather than total compensation. Employers could respond to these laws by changing the terms of jobs in order to have more cash pay and fewer fringe benefits, such as medical benefits, flexible work schedules or opportunities for training.
But because employers would be making the job changes to satisfy a regulation rather than for business reasons, the net result would still be fewer jobs for low-wage workers.