What would happen would depend on the amount to which the tax cut actually moves the aggregate supply (AS) curve and the aggregate demand (AD) curve.
If the tax cut only caused the AS curve to move, there would be lower prices and higher output. This is because AS would rise. But if AD moves as well, things could be different. This depends on how much AD rises (a tax cut would cause an increase in AD) relative to AS. If AD rose only a little compared to AS, output (real GDP) would increase while the price level would drop or perhaps stay the same. But if AD rose a great deal, there would be inflation. There would still be growth in real GDP, but the price level would rise as well.