The sign on the card and the English name for it come from two different suit systems, and the mismatch is visible every time the deck is dealt.
The sign is a clover
In French the suit is trefle, a clover leaf, and the shape on the card is a three-lobed leaf on a short stem. Nothing about the drawing suggests a weapon.
The name is Italian
English calls the suit clubs, from bastoni, the batons or cudgels of the Italian and Spanish Latin-suited packs. When French-suited cards displaced Latin-suited ones in England, the older suit name stayed attached to the slot the new sign occupied. The same thing happened with spades, from Italian spade, meaning swords. Two of the four English suit names therefore describe objects that are not on the cards.
Why the French signs won
The French pattern of the later fifteenth century replaced pictorial suits with four flat silhouettes in two colours that could be printed with stencils rather than engraved. Cheapness, not symbolism, is why this pattern became the international standard while the German and Latin patterns remained regional.
In cartomancy
Readers map this sign onto the baton suit of the Latin packs, which is where its association with work, enterprise and action comes from. That is a convention of reading rather than a derivation, and the atlas records it as one.