How could the supergiant military station of 180 km diameter reduce to dust a cosmic body that is hundredfold the station itself?

E = m c^2

Converting even a small fraction of its mass into energy would be sufficient.

If the station had the same average density as water at 1 bar and you were to accelerate the entire thing to light speed it would have an energy of 2.59 * 10^31 J. To put that another way that is 294,138,058,495,685,800 atomic bombs like the one dropped over Nagasaki.

Merry Christmas