Sharpen your axe on a grinding wheel. The grinding wheel is made of a much harder material than the iron or steel the axe head is made from. This will cause little pieces of the steel to fly from the axe causing a shower of sparks.
Chop wood with the axe. Many trees will have small mineral deposits that have been trapped in them while growing. When the axe strikes the mineral deposits, it will cause a spark from the blade as little chips of steel are released from the head of the axe.
Strike a glancing blow across a hard stone surface. The reason that steel sparks against flint is because the flint is much harder than the steel surface. Many rocks found throughout the landscape are harder than the metal of the axe head, chipping little pieces of steel from the axe as it strikes.