On this page of the Mr. Prepper guide, you will find information on how to get an axe.
Axe in Mr. Prepper comes in handy in the 4th and higher levels of the forest. With its help, you will unlock the paths in the forest blocked by downed trees. This way, you will also get large quantities of this resource.
You can find your first axe accidentally in the desert during car travels. It is also sold by Joe from the Junkyard, which you unlock after bringing Bob the jacket from the Mine.
When an axe's durability begins to drop, you should disassemble it at the workbench – this way you will get its blueprint.