Is this the correct use of Blockquote, q and cite?
<p>
<blockquote>Type HTML in the textarea above, <q>and it will magically appear</q> in the frame below.
</blockquote>
<cite><a href="http://stackoverflow.com">refrence url</a>
</p>
Is use of Blockquote, q semantically correct? or both are presentational element , so should not be used?
Yes. They are not presentational elements — blockquote represents a block quotation, q represents an inline quotation, and cite represents a reference to a name, work, standard, URL, etc.
You do have some validation errors that are fairly common with blockquote. A blockquote element cannot be inside a paragraph, and in HTML4 actually needs to contain paragraphs. The nesting of the p and blockquote elements in your fragment needs to be reversed.
The blockquote element (also the q element) can optionally have a cite attribute to specify a URI where the quote came from. HTML5 says user agents should make that link available to the user, and HTML4 doesn't say anything at all. I would include the URI both in the cite attribute and as an inline link, since browsers don't handle it.
Here's how I would write that fragment, with those revisions in mind:
<blockquote cite="http://stackoverflow.com">
<p>Type HTML in the textarea above, <q>and it will magically
appear</q> in the frame below.</p>
</blockquote>
<p>
<cite><a href="http://stackoverflow.com">reference url</a></cite>
</p>