Here's another possibility: elephants often do carry sticks of all sizes in their trunks, and some clever type may have decided to train them to carry a sword in their trunk in place of a stick.
I doubt that the elephant could be trained to effectively chop with that sword, but it might have been psychological weapon--the war elephant would be carrying a sword and waving it around and trumpeting, while the soldiers in the pagoda did something more effective with their weapons.
In that case, all an elephant sword would have to be is heavily built enough to survive being banged around by the elephant. Having it sharp might have even been an impediment.
As I noted above, training an elephant to kill people could be a really bad idea. It's easy enough for them to kill us without training, and trained killer elephants would be dangerous at all times, not just on the battlefield. That said, someone could put spikes on the tusks to make them better weapons, without training the elephant to do anything special with them.
Anyway, there is a problem with an elephant using a sword with its trunk. It would have a hard time getting enough leverage to cut with it. To see what problem is, take a kitchen knife (or a pocket knife), hold it only with your index finger curled around the hilt, and try cutting something. The elephant's trunk is more versatile than a single finger, but I think they've got the same problem.
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