Apply empty style to the entire bibliography

I would just separate the heading from the bibliography and put your page style commands in between:

\documentclass{memoir}
\usepackage[style=ieee, citestyle=numeric-comp, backrefstyle=none]{biblatex}
\addbibresource{biblatex-examples.bib}
\begin{document}
\tableofcontents
\nocite{*}
\printbibheading[heading=bibintoc]
\thispagestyle{empty}
\pagestyle{empty}
\printbibliography[heading=none]
\end{document}

This might be regarded as a fault with the standard bibliography environment in biblatex. In an article class what you are asking is no really appropriate as the bibliography is not designed to start on a separate page. But your problem persists in book and memoir, and the solution below works in all cases.
Namely, I patch (updated: better than previous redefining) the default biblatex default version of the bibliography environment to add a \clearpage efter the end of the bibliography's internal list environment.

\documentclass{book}

\usepackage[utf8]{inputenc}
\usepackage[
    backend=biber,
    style=ieee,
    citestyle=numeric-comp,
    backrefstyle = none
]{biblatex}

\renewcommand{\bibsetup}{\thispagestyle{empty}\pagestyle{empty}}

\addbibresource{biblatex-examples.bib}

\makeatletter
\patchcmd{\blx@endenv@bibliography}{\endlist}{\endlist\clearpage}{}{}
\makeatother

\title{Minimal working example}

\begin{document}

\section{Introduction}
\nocite{*}

\printbibliography[heading=bibintoc]

\end{document}

If you are in an article class, you will want to add \clearpage before \printbibliography