What do these curly graphics represent on this map?

The curly S shaped symbol, called an "area brace symbol" was used to indicate that the two properties actually share the same property number. It's possible that it was all once considered one property but the middle bit was subdivided and the two properties on the side maintain the same number.

The symbol is also called a "field tie" and sometimes called a "Vinculum". Though, I don't know how common the latter is.

Wikipedia states that Vinculum, which is also used in mathematics, is Latin for "bond", "fetter", "chain", or "tie", which is suggestive of some of the uses of the symbol.

Just to add some more information about vinculums (vinvulae?) as I recently encountered some of these, too. Land Information New Zealand has a FAQ which has the following section:

Why are some parcels not contiguous (ie they are separated by other parcels)?

Multi-polygons exist primarily for parcels that have a single survey appellation but may be physically divided. They are therefore in the same title (where a title exists). A common example is where a road cuts through a parcel, but two individual parcels were not created on the survey. On old survey plans, these would be shown with the parcels linked together with a vinculum (a symbol like a broken ‘s’). Under the Rules for Cadastral Survey 2010, surveyors are no longer allowed to create new multi-polygon parcels.

Judging by your map snippet, perhaps the mine divided a parcel of land, which was not subsequently redivided into two sections.

Source: http://www.linz.govt.nz/data/linz-data-service/linz-data-service-faqs