How to remove the last line-feed raised by \foreach

A listofitems alternative...

\documentclass{article}
\usepackage{listofitems}
\begin{document}
\readlist*\mylist{str1,str2,str3}
\framebox{%
  \parbox{4em}{%
    \foreachitem\x\in\mylist[]{%
      \makebox[4em][l]{\x}%
      \ifnum\xcnt<\mylistlen\relax\\\fi%
    }%
  }%
}
\end{document}

or switch the test order:

\documentclass{article}
\usepackage{listofitems}
\begin{document}
\readlist*\mylist{str1,str2,str3}
\framebox{%
  \parbox{4em}{%
    \foreachitem\x\in\mylist[]{%
      \ifnum\xcnt=1\relax\else\\\fi%
      \makebox[4em][l]{\x}%
    }%
  }%
}
\end{document}

The problem is that you issue a \\ at the end of each line. You can avoid it e.g. with

\documentclass{article}
\usepackage{tikz}

\begin{document}
\def\mylist{str1,str2,str3}

\framebox{
  \parbox{4em}{%
    \foreach \X [count=\Y]in \mylist {%
      \ifnum\Y=1
        \makebox[4em][s]{\X}
      \else 
        \\ \makebox[4em][s]{\X}%
      \fi
    }%
  }
}

\end{document}

With a conditionnal (minimum code text)

\documentclass{article}
\usepackage{tikz}

\begin{document}

\def\mylist{str1,str2,str3}
\framebox{
  \parbox{4em}{%
    \foreach \x[count=\n] in \mylist {%
      \ifnum \n >1 \\ \fi
      \makebox[4em][s]{\x}%
    }%
  }
}

\end{document}

With an array (just for the fun of it)

\documentclass{article}
\usepackage{tikz}

\begin{document}
\def\mylist{str1,str2,str3}
\def\before{{"\noexpand\\",{}}}
\framebox{
  \parbox{4em}{%
    \foreach \x[count=\n from 0] in \mylist {%
      \pgfmathparse{\before[!\n]}\pgfmathresult
      \makebox[4em][s]{\x}%
    }%
  }
}

\end{document}

Without any conditional ....

\documentclass{article}
\usepackage{tikz}

\begin{document}
\def\mylist{str2,str3}

\framebox{
  \parbox{4em}{%
   str1
    \foreach \x in \mylist {%
      \\\makebox[4em][s]{\x}%
    }%
  }
}

\end{document}