Rashi: The enemy will know that when it strikes on the gates of the openings of the Mikdash, it is like bringing its blows above in Shamayim. How will it know? It saw that the wood (ax-handle) held the ax blades and swallowed them ¹ . "Bi'Svach" is like "Ne'echaz ba'Sevach" (Bereishis 22:13). The wood intertwines them, and they are caught in it.

Radak: When the Beis ha'Mikdash was built, they knew who brought the axes in a thicket of wood, to cut it for the needs of building, as if he brought it above in front of Kisei ha'Kavod. This shows how much they rejoiced and glorified themselves about the building. Now the enemy came and struck with axes!

Malbim #1: This is how the enemy will know that destroying the Mikdash below displeases Hashem - if the axes are swallowed in the wood, and they cannot function.

Malbim #2: If the axes striking wood are swallowed in the wood, they will know [that Hashem is displeased]. Initially, this happened (refer to 74:5:1:1*), just later, the miracle ceased, and they made their signs [that Hashem agrees to the Churban].