Update
Since KOMA-Script version 3.26 you can also use the new key afterindent=false¹ and a positive beforeskip to get the desired result.
Example:
\documentclass{scrartcl}
\RedeclareSectionCommands[
afterindent=false,
beforeskip=1.5em,
afterskip=3pt
]{section}
\RedeclareSectionCommands[
afterindent=false,
beforeskip=1em,
afterskip=3pt
]{subsection,subsubsection}
\usepackage{blindtext}% only for dummy text
\begin{document}
\section{Section Title}
\Blindtext[2]
\subsection{Subsection Title}
\Blindtext[2]
\subsubsection{Subsubsection Title}
\Blindtext[2]
\section{Another Section Title}
\Blindtext[2]
\end{document}
The result is the same as in the original answer below.
¹Default setting is afterindent=bysign which results in the same behavior as in the original answer.
Original answer
From the KOMA-Script documentation:
beforeskip (length): The absolute value of the vertical skip before the heading.
If the value is negative, then the paragraph indent of the
text following the heading is suppressed.
So you have to add a - in front of the beforeskip values.
Example:
\documentclass{scrartcl}
\RedeclareSectionCommands[
beforeskip=-1.5em,
afterskip=3pt
]{section}
\RedeclareSectionCommands[
beforeskip=-1em,
afterskip=3pt
]{subsection,subsubsection}
\usepackage{blindtext}% only for dummy text
\begin{document}
\section{Section Title}
\Blindtext[2]
\subsection{Subsection Title}
\Blindtext[2]
\subsubsection{Subsubsection Title}
\Blindtext[2]
\section{Another Section Title}
\Blindtext[2]
\end{document}

Additional remark: If you use a negative value for afterskip, you will get a run-in heading.
beforeskip=-1.5emandbeforeskip=-1em. The-means that the first paragraph after the heading should not be indented. – esdd Mar 04 '18 at 19:22