If you click on a map in the plot window in Surfer to delete it, you will most likely select the layer and not the map frame. You can see this in the Contents window. The layer is the map type, ie. Contours, and the map frame is the entire map (called Map by default).
If you only have one layer in the map, and you select and delete that layer (either in the plot window or the Contents window), then the entire map is deleted.
If you have multiple map layers in the map, and you select a layer and delete it, then only that layer is deleted leaving the rest of the layers and the map frame still existing. To delete an entire map with multiple layers in Surfer, select Map from the Contents window and press DELETE on the keyboard (or right click over Map and click Delete).
See also: What is the difference between a "map frame" and a "map layer"?
Updated January 17, 2017