A character whose Strength is lower than the weapon die can use the weapon, but there are penalties. First, the weapon die can't be higher than his Strength die. So if a scrawny kid (d4 Str) picks up a long sword (d8), he rolls 2d4 damage, not d4+d8. A brawny hero with Str d10 rolls d10+d8 when using the same long sword.

Second, if the Strength die isn't at least equal to the weapon die, the attacker doesn't get any of the weapon's inherent bonuses, such as +1 Parry or Reach. He still retains any penalties, however (like -1 Parry).

If a weapon has a damage listed as Str+d8+2, for instance, then the minimum Strength the wielder must have is a d8.

Some ranged weapons list a minimum Strength to use as well. A character with a lower Strength can use the weapon, but suffers a -1 penalty to his attack roll for every step of difference between his Strength and the minimum Strength required. The penalty is ignored if the weapon can be braced on a bipod or other support.

Savage Worlds Deluxe Edition p. 54