cut completely and paste an element

appendTo() will automatically move the matched elements from their current location to the specified container, which seems to be what you want.

You can use after() to insert new content before moving the element:

$("#yourElement").after("<p>Element was there</p>").appendTo("body");

.detach() is more appropriate for this task, as @lvan suggested.

jQuery(jQuery("#yourElement").detach()).appendTo("body");

you can do it by clone first copy it to another location

$('#yourElement').clone().appendTo('#anotherDiv');

then remove old one,

 $('#parentOfOldElement #yourElement').remove();

or you can replace it to get it later

  $('#parentOfOldElement #yourElement').replaceWith('<div id="toReplaceAgain">/div>');