EDIT: Sorry, have discovered this feature now on the roadmap, but perhaps my suggestion beneath is worth to discuss.
I'm using Illustrator among others to draw font icons.
Each icon is on his own artboard / page for using the export-to-svg option (which is a pain to use each time you changed an icon).
Wish I could use slices instead in Designer and do an simple export like it can be done with Bitmaps.
The auto-export such a great idea, that it would be great for other export file types.
I know there's a difference because if you not fully enclose an vector element it's not a problem to save a sliced bitmap.
Suggestion: What if using slices on vectors just like the "crop" tool?
So if a slice doesn't enclose a vector fully, this cropped vector (with the boundaries of the slice) is saved as SVG.
PS: Thanks for your hard work! – I'm exploring Designer since yesterday and it's a pleasure to work with.