What permits and/or legal documents do I need to start a scissor/knife sharpening mobile business?

You will likely want to form a business entity (LLC or S-Corp), open a business bank account and do several other things to start doing proper business accounting. In addition, you should check with your local municipality about the required business licenses, etc. So, it would be wise to consult both with a local business attorney to help you determine what type of business entity you need and to help you properly form the same. You should also retain a good accountant to help you do proper business accounting correctly from the start. You will likely find that money spent on such professionals is money well spent and will save you FAR MORE in penalties and problems later. Best of luck!