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. If you press DELETE, you will only delete the selected layer, not the map frame (the map frame includes the axes). You can see the selected item in the Contents window.
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 and all the axes are 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 (including the axes) visible. 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 October, 2021