Mixed print and online save the dates?

Canva.com is a website where you can create or use templates for anything including invitations. I use them for posters for work. There are free ones. You can download them once created and it’s in png format. So, you could send it as an attachment in an email or save to a stick and print from a picture place. Or, you can order prints from them. Not sure how much that costs because I’ve never ordered prints.

When I was going to do that (will be sending out invitations only at this point) I was planning on just making one online and then printing it off on thick paper so it would be the exact same. I assume you could do it the opposite way as well where you get hard copies and then copy them to your email and send them out that way too.

Unfortunately I don't know of any service that will allow you to have a digital copy (high resolution, anyways, you can always screen shot your preview)...

You may need to design your own, so you have the digital copy, and then get Staples or something to print some for you.

I'm not 100% sure, but I believe you can achieve that via paperless post.
What you can also do is pick a simple save the date from paperless post to be sent via email. Then recreate the save the date via canva.com and have them printed through vistaprint.

Best of luck