Edit:
With 45 degrees angle (but if their angle is already 45,135,225 or 315 it will give a straight line)
I used the command of @AlanMatthes from here
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine}
\def\tikz@AngleOfLine(#1)(#2)#3{%
\pgfmathanglebetweenpoints{%
\pgfpointanchor{#1}{center}}{%
\pgfpointanchor{#2}{center}}
\pgfmathsetmacro{#3}{\pgfmathresult}%
}
%Command \diagconnect
% #1 is the arguments of \draw command like, red, thick etc
% #2 is the optional argument of the fraction of the horizontal distance for the break according to the horizontal distance of the points
% #3 and #4 are the points to be connected
\newcommand{\diagconnect}[3][-,red,thick]{
\tikzAngleOfLine(#2)(#3){\Angle}
\xdef\PerfectAngle{0}
\foreach \x in {45,135,225,315} {\ifdim\dimexpr \Angle pt\relax=\dimexpr\x pt\relax\xdef\PerfectAngle{1}\fi}
\ifnum\PerfectAngle=0
\ifdim\dimexpr\Angle pt \relax< \dimexpr90 pt\relax\relax
\draw[#1] let\p1=(#2),\p2=(#3) in (#2)-- ($(#2)+({(\x2-\x1)-abs(\x2-\x1)/(\x2-\x1)*abs(\y2-\y1))/2},0)$)--($(#3)-({(\x2-\x1)-abs(\x2-\x1)/(\x2-\x1)*abs(\y2-\y1))/2},0)$)--(#3);
\else
\draw[#1] let\p1=(#2),\p2=(#3) in (#2)-- ($(#2)+(0,{(\x2-\x1)-abs(\x2-\x1)/(\x2-\x1)*abs(\y2-\y1))/2})$)--($(#3)-(0,{(\x2-\x1)-abs(\x2-\x1)/(\x2-\x1)*abs(\y2-\y1))/2})$)--(#3);
\fi
\else
\draw[#1] (#2)--(#3);
\fi
}
\begin{document}
\begin{tikzpicture}
\node[rotate=45,anchor=west] (Point1) at (0,0){Point 1};
\node[rotate=45,anchor=west] (Point2) at (1,3) {Point 2};
\node[rotate=45,anchor=west] (Point3) at (4,0){Point 3};
\node[rotate=45,anchor=west] (Point4) at (7,1) {Point 4};
\diagconnect{Point1}{Point2};
\diagconnect{Point3}{Point4}
\node[rotate=45,anchor=west] (Point5) at (0,-4){Point 5};
\node[rotate=45,anchor=west] (Point6) at (2,-6) {Point 6};
\node[rotate=45,anchor=west] (Point7) at (4,-4){Point 7};
\node[rotate=45,anchor=west] (Point8) at (5,-7) {Point 8};
\diagconnect{Point5}{Point6};
\diagconnect{Point7}{Point8}
\node[rotate=45,anchor=west] (Point9) at (9,0){Point 9};
\node[rotate=45,anchor=west] (Point10) at (9,2) {Point 10};
\node[rotate=45,anchor=west] (Point11) at (7,-4){Point 11};
\node[rotate=45,anchor=west] (Point12) at (9,-4) {Point 12};
\diagconnect{Point9}{Point10};
\diagconnect{Point11}{Point12}
\end{tikzpicture}
\end{document}

Old answer (but useful in other cases):
You can define a newcommand
with an extra argument (except the \draw options that is optional and the two points that are required) that will be the fraction of the horizontal distance of the points that you want this "break".
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
%Command \diagconnect
% #1 is the arguments of \draw command like, red, thick etc
% #2 is the optional argument of the fraction of the horizontal distance for the break according to the horizontal distance of the points
% #3 and #4 are the points to be connected
\newcommand{\diagconnect}[4][]{\draw[#1] let\p1=(#3),\p2=(#4) in (#3)-- ($(#3)+({abs(\x2-\x1)/(\x2-\x1)*abs(\x2-\x1)*#2},0)$)--($(#4)-({abs(\x2-\x1)/(\x2-\x1)*abs(\x2-\x1)*#2},0)$)--(#4);}
\begin{document}
\begin{tikzpicture}
\coordinate (Marmot) at (0,1);
\coordinate (Duck) ate (2,0);
\draw (Marmot) -- (Duck);
\draw (Marmot) |- (Duck);
%\draw[red] (Marmot) -- (0.5,1) -- (1.5,0) -- (Duck);
\diagconnect[thick,red]{0.3}{Marmot}{Duck}
\node[rotate=45,anchor=west] at (Marmot) {Marmot Burrow};
\draw (Marmot) circle (0.05);
\node[rotate=45,anchor=west] at (Duck) {Duck Pond};
\draw (Duck) circle (0.05);
\end{tikzpicture}
\end{document}
Output:
