That doesn't make any sense, businesses don't hire people on a whim, they hire people because they have roles that need doing, minimum wage doesn't change that.
Businesses hire people when they have a job that needs doing, provided that it's worth the cost. Not every potential job is worth its cost, and minimum wage artificially raises that cost, with the obvious result that some jobs simply go undone.
There is also the matter of competition which is not subject to the minimum wage—not just under-the-table employment and offshoring, but also automation. With the increased minimum wage, businesses may find that it's now cheaper to employ a machine, where before they would have given the job to a human. Or perhaps they simply increase their existing employees' workloads rather than hiring someone else to handle the "unskilled" jobs.
Even if every business did act like it was insensitive to wages, as you seem to think, that would just mean that the marginal ones are no longer profitable and thus go out of business, further reducing both the supply of goods and the demand for labor.