TikZ: clipping inside the box

Question

I can clip everything that is outside of a box

\documentclass{article}

\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[]
\clip (-1, 0) rectangle (1, 1);
\draw (0, 0) circle (2 and .5);
\end{tikzpicture}
\end{document}

But how can I go about clipping things that are inside a rectangle, and drawing only things that are outside of the rectangle ?

I can clip with a complicated polygon

\documentclass{article}

\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[]
\clip (-1, 0) -- (1, 0) --  (1, 1) -- (3, 1) -- (3, -1) -- (-3, -1) -- (-3, 1) -- (-1, 1) -- (-1, 0) -- cycle;
\draw (0, 0) circle (2 and .5);
\end{tikzpicture}
\end{document}

But is there a simpler way to do this?

Answer 1

There are several posts on even odd clip and reversclip` that can be used here.

\documentclass{article}
\usepackage{tikz}
% based on 
% https://tex.stackexchange.com/a/38995/121799 
% https://tex.stackexchange.com/a/76216 
% https://tex.stackexchange.com/a/59168/194703 
% https://tex.stackexchange.com/q/448920/194703 
\tikzset{even odd clip/.code={\pgfseteorule},
reverseclip/.style={overlay,insert path={(-16383.99999pt,-16383.99999pt) rectangle (16383.99999pt,16383.99999pt)}}}

\begin{document}
\noindent
\begin{tikzpicture}[]
\draw (-1, 0) rectangle (1, 1);
\draw (0, 0) circle (2 and .5);
\end{tikzpicture}

\noindent
\begin{tikzpicture}[]
\path[save path=\pathA] (0, 0) circle (2 and .5);
\clip[overlay,even odd clip,reverseclip] (-1, 0) rectangle (1, 1) ; 
\draw[use path=\pathA] (0, 0) circle (2 and .5);
\end{tikzpicture}
\end{document}