You can use the following
\documentclass{minimal}
\usepackage{mathspec}
\setmainfont{DejaVu Sans}
\setmathsfont(Digits,Latin,Greek){DejaVu Sans}
\setmathrm{DejaVu Sans}
% 0 (large) \mathop, 1 (binary) \mathbin, 2 (vary) \mathbin, 3 (relation) \mathrel, 4 (opening) \mathopen, 5 (closing) \mathclose, 6 (punctuation) \mathpunct, 7 (alphabetic) \mathalpha
\Umathcode`=="3 \csname symLatin:m:n\endcsname `=
\Umathcode`-="2 \csname symLatin:m:n\endcsname `-
\Umathcode`×="2 \csname symLatin:m:n\endcsname `× \def\times{×}
\begin{document}
\(\mathrm{e}^{\mathrm{i}\pi}=-1\) = -1
\end{document}
giving

as requested.
However, note that -
is U+002D HYPHEN-MINUS
and there is also −
U+2212 MINUS SIGN
, which you might want to use instead:

For this, replace the relevant line by
\Umathcode`-="2 \csname symLatin:m:n\endcsname `−
(last character in line being U+2212 MINUS SIGN
).
I learned this from @egreg's answer to my question Symbols in XeLaTeX.