The picture above shows the demolition of the 1885 Mortimer Building in the summer of 1919. This was a substantial building when constructed, designed by George Post, one of New York’s premier architects in the late nineteenth century, and occupied by firms involved with banking and trading. It’s not obvious from this photo, but the building was adjacent to the New York Stock Exchange. The rear of the NYSE is the facade on the far right, facing New Street, and there’s a one-bay sliver of a wing facing Wall Street just to the left of Mortimer. The rear of the NYSE doesn’t look much different from any other office building; it’s the Broad Street front that has the huge Roman-temple pediment.
The location adjacent to the NYSE is why the building was being demolished. The exchange was looking to expand and there were only so many possible locations adjacent to its 1903 building, also designed by Post. The site just to the north was occupied by Mortimer, the narrow NYSE wing, and the Wilks Building, an 1890 proto-skyscraper or early skyscraper depending on your feelings about several technical topics. Here’s the demolition of Wilks, with its three-story mansard roof already removed:

And here’s the site cleared, with the side wall of the NYSE on the far left.

It’s probably easier to understand by looking at a 1905 Sanborn map:

The tan color indicates that the buildings are “fireproof” (or, in the case of Wilks, “semi-fireproof”), the blue indicates stone facades. The building at the bottom, running through the block from New Street on the left to Broad Street on the right is the NYSE.
These were bearing-wall buildings with very heavy masonry walls and tile-arch floors. Demolishing them was undoubtedly tedious, although the dates on the photos suggest it wasn’t particularly slow.