hack, chop, cut, fell
砍 centers on forceful cutting with a heavy tool: hacking, chopping, felling trees, or cutting through something tough.
砍 combines 石 (stone) and 欠 (a pictograph of a person with an open mouth, later associated with lack or action). The exact historical development is uncertain, but the character likely expresses cutting or hacking with a stone tool.
A stone (石) axe is used to hack and chop, with the right side (欠) looking like a person swinging a tool. Imagine a stone blade cutting through wood.
For カン, picture a can of food being hacked open with a stone: can -> カン, and the stone blade chops through the metal.