Unfortunaly there is no MWE in the question. So I do not know if scrartcl, scrreprt, scrbook or another class is used.
scrlayer-scrpage
Note that package scrpage2 is outdated. With its successor scrlayer-scrpage you can disable plainheadsepline using \KOMAoptions{plainheadsepline=false} and enable it again using \KOMAoptions{plainheadsepline}.
In the following example the plainheadsepline is disabled locally.
\documentclass[headsepline]{scrreprt}
\usepackage{blindtext}% dummy text
\usepackage[automark,plainheadsepline]{scrlayer-scrpage}
\begin{document}
\tableofcontents
\clearpage
\pagenumbering{roman}
\begingroup
\KOMAoptions{plainheadsepline=false}
\pagestyle{plain}
\addsec{Acknowledgement}
\Blindtext
\clearpage
\addsec{Abstract}
\Blindtext
\clearpage
\endgroup
\blinddocument
\end{document}

scrpage2 (outdated)
With the older package scrpage2 you can not disable plainheadsepline. As a workaround you can change the width of the headsepline to 0pt.
\documentclass[headsepline]{scrreprt}
\usepackage{blindtext}% dummy text
\usepackage[automark,plainheadsepline]{scrpage2}
\pagestyle{scrheadings}
\begin{document}
\tableofcontents
\clearpage
\pagenumbering{roman}
\begingroup
\setheadsepline{0pt}
\pagestyle{plain}
\addsec{Acknowledgement}
\Blindtext
\clearpage
\addsec{Abstract}
\Blindtext
\clearpage
\endgroup
\pagenumbering{arabic}
\blinddocument
\end{document}

Because of a comment here are additional examples with article class:
scrlayer-scrpage
\documentclass{article}
\usepackage{blindtext}% dummy text
\usepackage[automark,headsepline,plainheadsepline]{scrlayer-scrpage}
\begin{document}
\tableofcontents
\clearpage
\pagenumbering{roman}
\begingroup
\KOMAoptions{plainheadsepline=false}
\pagestyle{plain}
\section*{Acknowledgement}
\Blindtext
\clearpage
\section*{Abstract}
\Blindtext
\clearpage
\endgroup
\blinddocument
\end{document}
scrpage2 (outdated)
\documentclass{article}
\usepackage{blindtext}% dummy text
\usepackage[automark,headsepline,plainheadsepline]{scrpage2}
\pagestyle{scrheadings}
\begin{document}
\tableofcontents
\clearpage
\pagenumbering{roman}
\begingroup
\setheadsepline{0pt}
\pagestyle{plain}
\section*{Acknowledgement}
\Blindtext
\clearpage
\section*{Abstract}
\Blindtext
\clearpage
\endgroup
\pagenumbering{arabic}
\blinddocument
\end{document}
KOMAoption{plainheadsepline}{no}andKOMAoption{plainheadsepline}{yes}as needed. Untestet of course. – Johannes_B Mar 20 '16 at 16:49