Intricate Topiaries are structures exclusive to the Hamlet DLC, spawning naturally in the Pig Citybiome. There are 4 different topiaries, each of which may spawn with their own "build" of surrounding structures (as a Set Piece would).
The Intricate Topiaries can be destroyed with a hammer, however they do not get fully removed. They can be repaired again by the player using a hammer, or by a nearby worker Pig.
To fully remove the Intricate Topiary, one must obtain the Executive Hammer from the Palace. There is currently no way to reconstruct the Intricate Topiaries.
According to Rhymes with Play #213, the designs of the Intricate Topiaries might be lore-relevant.