Separate table of contents for appendix

Here is a solution using etoc package

\documentclass{scrbook}
\usepackage{etoc}

\begin{document}
\etocdepthtag.toc{mtchapter}
\etocsettagdepth{mtchapter}{subsection}
\etocsettagdepth{mtappendix}{none}
\tableofcontents‎‎
\chapter{First chapter}
text text text

\section{A section}
text text text

\subsection{A subsection}
text text text

\appendix

\etocdepthtag.toc{mtappendix}
\etocsettagdepth{mtchapter}{none}
\etocsettagdepth{mtappendix}{subsection}
\tableofcontents‎‎
\chapter{Appendix A}
text text text

\section{Specific}
text text text

\subsection{A subsection}
text text text

\end{document}

Update Here is a suggestion without any additional package, but it needs KOMA-Script version 3.23 or newer.

\documentclass[appendixprefix]{scrbook}[2017/04/13]

\DeclareNewTOC[%
  owner=\jobname,
  listname={\contentsname~(\appendixname)},% title of the appendix ToC
]{atoc}

\makeatletter
\newcommand*\appendixwithtoc{%
  \appendix
  \renewcommand*{\ext@toc}{atoc}%
  \scr@ifundefinedorrelax{hypersetup}{}{\hypersetup{bookmarkstype=atoc}}%
  \listofatocs
}
\makeatother

\usepackage{blindtext}
\begin{document}
\tableofcontents
\chapter{Chapter I}
\section{Section I}
\chapter{Chapter II}

\appendixwithtoc
\chapter{Annex I}
\section{Section of Annex I}
\chapter{Annex II}
\end{document}

---

Original answer

Here is another suggestion using the KOMA-Script package scrwfile:

\documentclass[appendixprefix]{scrbook}
%
\usepackage{scrwfile}
\TOCclone[\contentsname~(\appendixname)]{toc}{atoc}
\newcommand\StartAppendixEntries{}
\AfterTOCHead[toc]{%
  \renewcommand\StartAppendixEntries{\value{tocdepth}=-10000\relax}%
}
\AfterTOCHead[atoc]{%
  \edef\maintocdepth{\the\value{tocdepth}}%
  \value{tocdepth}=-10000\relax%
  \renewcommand\StartAppendixEntries{\value{tocdepth}=\maintocdepth\relax}%
}
\newcommand*\appendixwithtoc{%
  \cleardoublepage
  \appendix
  \addtocontents{toc}{\protect\StartAppendixEntries}
  \listofatoc
}
%
\usepackage{blindtext}
\begin{document}
\tableofcontents
\chapter{Chapter I}
\section{Section I}
\chapter{Chapter II}

\appendixwithtoc
\chapter{Annex I}
\section{Section of Annex I}
\chapter{Annex II}
\end{document}