Without any idea about what you're going to do, it would be hard to make a suggestion about it, but sometimes the metal edging could be useful for certain separation and retention functions. (In some situations, it is barely or not at all visible when properly installed.) I would complete planning for the whole yard before I chucked it. If you're determined to get rid of it, you might advertise it for free on craig's and someone might dig it out for you.

Other than that, you should be able to pry it out of the ground with a sturdy, long-handled shovel. Excavate a little of it to see how it is attached with metal stakes.

Use a mattock - dig down enough to slide the blade under the bottom of the edging and start prying.

It's a lot of work ... i'd ignore it, and mulch over it.