A few points:
(a) Your title is confusing. Your question is not about xsl:copy-of. When asking a new question, please start a new thread.
And when asking any question, please show your input, your desired output, your attempt at solving it, and any error messages.
(b) I don't know what you mean by a "block of text". XSLT operates on trees, not on text. Do you mean you want to remove the <ats:MyDataItem> element and all its descendant nodes?
(c) "Using a blank template" suggests that you have got the basic idea that a template like <xsl:template match="ats:MyDataItem"/> causes this element not to be copied to the result tree.
(d) "has prefix" suggests that your problem is with namespaces, or at least that you think it is. But since you haven't shown any code, I can't tell what you have done wrong.
Michael Kay
http://www.saxonica.com/
Author, XSLT 2.0 and XPath 2.0 Programmer's Reference