Check out this [thread][1]:
It seems to have something to do with how your SVG file is formatted.
Using inscape, which saves it’s files in svg format. I was able to import all the curves as a single document, single layer, and sill have each element be individually selectable and adjustable.
So you may want to play with the export setting of whatever program / plugin you are using to create your SVG file.
[1]: How to cut multiple 2.5D shapes?