If my employer has a new rule that if an employee is even 1 minute late he will deduct a full hour's pay, is this legal?

Unfortunately, if you *truly* are an independent contractor, this could be legal--the relationship between an independent contractor and its customer/client is governed by the contract between them, and that includes the compensation, any non-performance penalties, etc. If there is no written contract, only an oral agreement, it is most likely the case that the employer can propose new terms and conditions at will.

If you were an employee, this would not be legal--hourly employees must be paid for all time worked, and the employer must keep accurate time records. Being late a minutes should mean losing 1/60th of an hour's pay.

From what you write, you may be an employee, not an independent contractor; it doesn't matter what you are called, all that matters is the relationship between you and the employer. Go the Department of Labor website to see the test or criteria for when someone is truly an independent contactor or not; in brief, an independent contractor has at least some degree of independence. If the employer is setting your hours down to the minute, you may not be an independent contractor.

If you actually are an employee and have been misclassified, not only can the employer not take an hour's pay away for 1 minute's lateness, but you may also be owed--both retroactively and for the future:

1) Overtime, if you work more than 40 hours in a week;

2) The employer share of FICA;

3) Benefits, if your employer provides them for  employees.

It's worth trying to see if you have been misclassified, therefore, since if you actually should be treated as an employee, you may be owed compensation.