Assuming it works, why on earth would you want to throw it away? If it isn't something that you don't want to wear anymore then give it to a charity shop, pass it on to a friend or young relative, or just stick it on Ebay as an auction starting at ÂŁ0.99p/99 cents. Absolutely no need at all to ever throw away a working watch.
And if you really don't know if it works then take it to your local battery change guy and see if a new cell makes it work.
Sent from my Nexus 7 using Tapatalk