Why did Kirito toss the sword away in episode 17 of the second season?
It's because the sword was overburdening Kirito and since he can't put it into his inventory, he had to make a choice of either letting it go so he can make the jump onto Tonkii or going down with it:
From the (previously translated) light novel (Sword Art Online Volume 8, Early and Late, Caliber, page 308):

At that point, I noticed one terrible fact.
I couldn't jump.
To be more exact, in my arms was a heavy load the «Holy Sword Excaliber», so jumping five meters wouldn't be possible. Just by standing, my boots already bit into the ice.