The job losses from a $15 minimum wage mean that it will not alleviate poverty, but will simply redistribute poverty. While poor workers who keep their jobs may be lifted out of poverty by a $15 minimum wage, other near-poor workers who lose their jobs or have their hours cut will be plunged into poverty. The misery just gets shuffled around.
Standard economic theory holds that when the costs of low-wage workers are raised by a higher minimum wage, employers reduce employment — for two reasons. First, employers suddenly find it economical to replace, say, two minimum-wage workers with one slightly more expensive, presumably more experienced or efficient worker. (One $25-an-hour worker may be a better deal than two $15-an-hour workers.) Second, the rising cost of salaries leads employers to raise prices, which leads to lower demand, meaning they have to lower overhead by reducing head count.