You could use memoir's \currenttitle:
\documentclass{memoir}
\usepackage{mdframed}
\mdtheorem[style=mpdframe]{discuss}{Discuss Topic}[chapter]
\begin{document}
\chapter{Test chapter}
\section{Test section}
\label{sec:test}
\begin{discuss}[\currenttitle]
test text
\end{discuss}
\end{document}

The problem with the above code is that \currenttitle stores the last sectional unit used, which might not be a section; in this case, some additional work will do; a patch to \M@sect was used to store the name of the current section in \currentsectionname:
\documentclass{memoir}
\usepackage{mdframed}
\mdtheorem[style=mpdframe]{discuss}{Discuss Topic}[chapter]
\makeatletter
\let\currentsectiontitle\relax
\patchcmd{\M@sect}
{\ifheadnameref}
{\ifnum#2=1\relax
\gdef\currentsectiontitle{#9}
\fi
\ifheadnameref}
{}
{}
\makeatother
\begin{document}
\chapter{Test chapter}
\section{Test section}
\label{sec:test}
\begin{discuss}[\currentsectiontitle]
test text
\end{discuss}
\end{document}
The definition for the mpdframe style was missing in the question.
As mentioned in a comment to the question, since this is going to be used for every discuss environment, I think it's better to use \newmdtheoremenv with a custom theorem style to automatically provide the current section title; something along these lines:
\documentclass{memoir}
\usepackage{amsthm}
\usepackage{mdframed}
\newtheoremstyle{mystyle}
{\topsep}
{\topsep}
{}
{}
{\bfseries}
{\newline}
{.5em}
{\thmname{#1}~\thmnumber{#2}: \currentsectiontitle}
\theoremstyle{mystyle}
\newmdtheoremenv{discuss}{Discuss Topic}[chapter]
\makeatletter
\let\currentsectiontitle\relax
\patchcmd{\M@sect}
{\ifheadnameref}
{\ifnum#2=1\relax
\gdef\currentsectiontitle{#9}
\fi
\ifheadnameref}
{}
{}
\makeatother
\begin{document}
\chapter{Test chapter}
\section{Test section one}
\subsection{Test subsection}
\label{sec:test}
\begin{discuss}
test text
\end{discuss}
\section{Test section two}
\subsection{Test subsection}
\label{sec:test}
\begin{discuss}
test text
\end{discuss}
\end{document}

Update after the edit to the question
The above suggestions won't work since the titlesec package is used (which might be not a good idea with the memoir class; see About memoir and titlesec incompatibility). In this case you can use:
\documentclass{memoir}
\usepackage{mdframed}
\usepackage[explicit]{titlesec}
\usepackage{tikz}
\usetikzlibrary{shapes.misc}
\mdtheorem[style=mpdframe]{discuss}{Discuss Topic}[chapter]
\makeatletter
\let\currentsectiontitle\relax
\newcommand\titlebar@{%sections
\tikz[baseline,trim left=3.1cm,trim right=3.0cm] {
\fill [black!15] (2.5cm,-1ex) rectangle (\textwidth+3.1cm,2.5ex);
\node [
fill=black!100!white,
anchor= base east,
rounded rectangle,
minimum height=3.75ex] at (3cm,0.01) {
\color{white}\textbf{T\thesection}
};
}}
\newcommand\titlebar@@{%osections
\tikz[baseline,trim left=3.1cm,trim right=3.15cm] {
\fill [black!15] (2.5cm,-1ex) rectangle (\textwidth+3.1cm,2.5ex);
\node [
fill=black!100!white,
anchor= base east,
rounded rectangle,
minimum height=3.75ex] at (3cm,0.15) {
};
}}
\newcommand\titlebar{@ifstar\titlebar@@\titlebar@}
\titleformat{\section}
{\large\bfseries}
{\titlebar}
{0.1cm}
{\gdef\currentsectiontitle{#1}#1}
\renewcommand{\thesection}{\arabic{section}}
\newcommand{\osection}[1]{\section{\titlebar*#1}}
\makeatother
\begin{document}
\chapter{Test chapter}
\section{Test section}
\label{sec:test}
\begin{discuss}[\currentsectiontitle]
test text
\end{discuss}
\end{document}

Or with the automatic inclussion via a new theorem style:
\documentclass{memoir}
\usepackage{amsthm}
\usepackage{mdframed}
\usepackage[explicit]{titlesec}
\usepackage{tikz}
\usetikzlibrary{shapes.misc}
\newtheoremstyle{mystyle}
{\topsep}
{\topsep}
{}
{}
{\bfseries}
{\newline}
{.5em}
{\thmname{#1}~\thmnumber{#2}: \currentsectiontitle}
\theoremstyle{mystyle}
\newmdtheoremenv{discuss}{Discuss Topic}[chapter]
\makeatletter
\let\currentsectiontitle\relax
\newcommand\titlebar@{%sections
\tikz[baseline,trim left=3.1cm,trim right=3.0cm] {
\fill [black!15] (2.5cm,-1ex) rectangle (\textwidth+3.1cm,2.5ex);
\node [
fill=black!100!white,
anchor= base east,
rounded rectangle,
minimum height=3.75ex] at (3cm,0.01) {
\color{white}\textbf{T\thesection}
};
}}
\newcommand\titlebar@@{%osections
\tikz[baseline,trim left=3.1cm,trim right=3.15cm] {
\fill [black!15] (2.5cm,-1ex) rectangle (\textwidth+3.1cm,2.5ex);
\node [
fill=black!100!white,
anchor= base east,
rounded rectangle,
minimum height=3.75ex] at (3cm,0.15) {
};
}}
\newcommand\titlebar{@ifstar\titlebar@@\titlebar@}
\titleformat{\section}
{\large\bfseries}
{\titlebar}
{0.1cm}
{\gdef\currentsectiontitle{#1}#1}
\renewcommand{\thesection}{\arabic{section}}
\newcommand{\osection}[1]{\section{\titlebar*#1}}
\makeatother
\begin{document}
\chapter{Test chapter}
\section{Test section one}
\subsection{Test subsection}
\begin{discuss}
test text
\end{discuss}
\section{Test section two}
\subsection{Test subsection}
\begin{discuss}
test text
\end{discuss}
\end{document}
