$(cont).remove("copy_btn").appendTo("body");
The problem here is that:
.remove( [ selector ] )
selectorA selector expression that filters the set of matched elements to be removed.
Hence the suggestion .find("#copy_btn").remove() is the way to go and according to documentation.
Of course you have to remember that after find(), your result set is now the <a> you're removing, so to go back to the previous matched set, you need .end()
Your final js looking like:
var cont = $('#container').clone();
$(cont)
.find("#copy_btn")
.remove()
.end()
.appendTo("body");