I would like to know if an employer in Fayetteville Arkansas has the right to take 10% of the employees gross cash sales from their tips at the end of their shift. This is the case with my wife, and not everyone tips 10%. It is usually less.

Is this a tip pooling arrangement where those tips are shared among other employees who regularly and customarily receive tips, such as bartenders, bussers, etc.? Or is the employer keeping them for himself? The first is legal; the second is not.
http://www.dol.gov/esa/regs/compliance/whd/whdfs15.htm

Does her cash wage plus the tips she retains average to at least the minimum wage per hour worked during a workweek?

She does not have to share tips, but they say it is for tax purposes. But if she is not making that 10%, are they not taking more from her then they should?

I'm sorry, I misunderstood the question. Are you saying they are reporting on the records that she received 10% of her gross sales in tips, even though she reports that she received less than that? No, they can't do that.

At the end of the year, if they need to allocate a shortfall of tips across the board to employees who did not claim at least 8% of gross wages in tips, that's a different issue; allocated tips such as in this specific law are W-2 wages only, they don't get recorded on the paychecks. But they cannot record more tips for purposes of her pay than she reported she took in.

If they are, she should file a complaint with the state Dept. of Labor.