How do I remove blank pages coming between two chapters in Appendix?

Your problem is that all chapters, whether they're in the appendix or not, default to starting on an odd-numbered page when you're in two-sided layout mode. A few possible solutions:

The simplest solution is to use the openany option to your document class, which makes chapters start on the next page, irrespective of whether it's an odd or even numbered page. This is supported in the standard book documentclass, eg \documentclass[openany]{book}. (memoir also supports using this as a declaration \openany which can be used in the middle of a document to change the behavior for subsequent pages.)

Another option is to try the \let\cleardoublepage\clearpage command before your appendices to avoid the behavior.

Or, if you don't care using a two-sided layout, using the option oneside to your documentclass (eg \documentclass[oneside]{book}) will switch to using a one-sided layout.

If you specify the option 'openany' in the \documentclass declaration each chapter in the book (I'm guessing you're using the book class as chapters open on the next page in reports and articles don't have chapters) will open on a new page, not necessarily the next odd-numbered page.

Of course, that's not quite what you want. I think you want to set openany for chapters in the appendix. 'fraid I don't know how to do that, I suspect that you need to roll up your sleeves and wrestle with TeX itself

You can also use \openany, \openright and \openleft commands:

\documentclass{memoir}
\begin{document}

\openany
\appendix

\openright
\appendixpage
This is the appendix.

\end{document}