Which stone age did they have stone axes?

There has only been one Stone Age. The Stone Age refers to the era when man learnt to make tools and weapons from rock and stone. The Stone Age was between 6,000 BC and 2,500 BC for the majority of humanity, though some of humanity came out of the Stone Age early upon discovering metals.

The three periods of the Stone Age are Palaeolithic, Mesolithic and Neolithic. It's difficult to determine exactly when stone axes started to appear exactly because different groups of humanity entered the Stone Age at different times. However it is believed the first axe may have been created during the middle of the Palaeolithic stage of the Stone Age.