Adobe Illustrator and Corel Draw should fundamentally work the same in terms of interacting w/ Easel: create path geometry, save to a .svg, open in Easel.
Start in Adobe Illustrator — go into outline mode — does the design look like a reasonable outline representation of what you want to cut or are there lots of extraneous paths / lines? If the latter, you have to use the tools in AI to get down to just what’s needed.
Try selecting something which you’d want to cut — did it select cleanly as a single object, or was only a part selected, or did you get more — that too will need to be addressed.
Once you’re down to a nice clean set of paths, if you have trouble exporting and importing that, post the file somewhere and we can work you through the balance of it.