Depends.
Currently, there are two money amounts an employer is interested in when paying an employee: how much the employee adds value to the employer, and how much the employer would have to pay to get a replacement worker. What the minimum wage does is raise the latter price for low-end employees.
For sake of example, assume that the wages are the only cost to the employer, an employer will be OK with making a slim profit, and we're discussing raising minimum wage from $10/hour to $15/hour. Currently, the employer has multiple employees that are easy to replace, and hence pays $10/hour for them. Some of them presumably have only $11 value to the employer, and others have much higher value. A kid who restocks the shelves might be completely replaceable, but the business can't run without that function, so other, higher paid, employees would have to do it. Call the value $25/hour. A similar case might be a fast-food cashier during lunch hour. In those cases, the employer simply pays the higher minimum wage.
I've oversimplified that a lot, and you'll have to throw in additional factors. (I'm probably costing my company twice my salary, but I get paid time off and various benefits, so we'd use a smaller factor for the usual minimum-wage worker.)
So, for best impact on employees, we need to raise the minimum wage as high as we can without exceeding the value added for most workers. Most of us aren't worth $100/hour to our employers, so that would throw most people out of work. There are tradeoffs, but it's not a matter of destroying all current minimum-wage jobs, and it's definitely a matter for empirical consideration.
The effects on businesses will vary. A business with low labor costs won't be affected much, and a business employing mostly people well above the minimum wage won't be affected much. Businesses that have high labor costs and employ mostly minimum-wage (or slightly more) employees will be hit with nearly full impact by the raise. Some such businesses compete primarily with other such businesses, and they will raise their prices and be somewhat less profitable, and some will compete primarily with businesses without that problem, and they will be hit harder, since they can't raise prices. Some businesses will go out of business, and we don't want to do that to too many businesses. Again, it's a tradeoff with consequences we need to find empirically.
If the minimum-wage worker is eligible for government low-income benefits because of low pay, then the government is subsidizing the employers, and I'd like to see that end. It's a market distortion caused by externalizing the cost of keeping the employees in shape to work.