pathfinder 1e – Trying to throw a large harpoon by a medium character?

There is nothing saying you’re not allowed to throw something with both hands, so yes, you can throw it. And it is not improvised—it’s a weapon, being used as intended, so it remains that weapon. If you tried to smack someone with the butt end of the harpoon, that would be an improvised usage, but here you’re trying to use it as it was made to be used.

So in the end, it’s exactly like making the same attack with a Medium harpoon with only these exceptions:

  • You must use 2 hands. This doesn’t affect your Strength bonus to damage, because the rule about adding 1½ Str to damage is for “one-handed weapons” (used in both hands) and “two-handed weapons” (also, of course, used in both hands), and “one-handed weapon” and “two-handed weapon” are designations for “melee weapons.” (Personally, as GM, I would allow two-handed throwing in sensible situations to get 1½ Str to damage but that’s not in the rules.)

  • You take a −2 penalty for the size mismatch.

  • The weapon’s base damage is 2d6 instead of 1d8.