How to switch of headsepline in KOMA Script for selfdefined pagestyle

You can use \KOMAoptions in the definition

\documentclass[a4paper,11pt,twoside]{scrbook}
\usepackage[manualmark,headsepline,footsepline]{scrlayer-scrpage}
\usepackage{blindtext}

\lehead{left even}
\cehead{center even}
\rehead{right even}

\lohead{left odd}
\cohead{center odd}
\rohead{right odd}

\newpairofpagestyles[scrheadings]{chapter}{%
\KOMAoptions{headsepline=false}%
\lehead*{}%
\cehead*{useless text}%
\cohead*{usefull text}%
\rohead*{}%
}

\renewcommand*\chapterpagestyle{chapter}

\begin{document}
\blinddocument
\end{document}

But I'm not sure if declaring a new paired pagestyle is the way to go. Why don't you redefine the plain style?

If you need different styles for TOC, chapter pages and normal pages, you can also use the plain style for your chapter pages with

\lehead{left even}
\cehead[useless text]{center even}
\rehead*{right even}

\lohead*{left odd}
\cohead[usefull text]{center odd}
\rohead{right odd}

and change the header and footer in TOC by

\BeforeTOCHead[toc]{%
    \clearpage
    \KOMAoptions{plainfootsepline=false}%
    \lehead[]{left even in toc}%
    \cehead[]{center even in toc}%
    \rehead[]{right even in toc}%
%
    \lohead[]{left odd in toc}%
    \cohead[]{center odd in toc}%
    \rohead[right on odd toc start page]{right odd in toc}%
}
\AfterStartingTOC[toc]{\clearpage}

Example:

\documentclass[a4paper,11pt,twoside]{scrbook}
\usepackage[
    manualmark,
    headsepline,
    footsepline,
    plainfootsepline% added to get a footline on plain pages
]{scrlayer-scrpage}
\usepackage{blindtext}
\usepackage{microtype}

\lehead{left even}
\cehead[useless text]{center even}
\rehead*{right even}

\lohead*{left odd}
\cohead[usefull text]{center odd}
\rohead{right odd}

\BeforeTOCHead[toc]{%
    \clearpage
    \KOMAoptions{plainfootsepline=false}%
    \lehead[]{left even in toc}%
    \cehead[]{center even in toc}%
    \rehead[]{right even in toc}%
%
    \lohead[]{left odd in toc}%
    \cohead[]{center odd in toc}%
    \rohead[right on odd toc start page]{right odd in toc}%
}
\AfterStartingTOC[toc]{\clearpage}

\begin{document}
\addchap{Introduction}
\Blindtext
\tableofcontents
\Blinddocument\Blinddocument\Blinddocument\Blinddocument
\Blinddocument\Blinddocument\Blinddocument\Blinddocument
\Blinddocument\Blinddocument
\end{document}

You could also use something like

\BeforeTOCHead{%
    \clearpage
    \KOMAoptions{automark}%
    \clearpairofpagestyles
    \chead[plain page in toc]{}%
    \ohead{\headmark}%
    \ofoot*{\pagemark}%
}
\AfterStartingTOC{\clearpage}

to use automark in TOC, LOT and LOF.