Datavisualization
I checked the documentation (Tikz Manual, VI. Data Visualization, page 851 in version 3.1.9a), but I couldn't find anything about this. So the only way would be for you to change the min value to the minimum you have in your coordinates.
This would yield this result:

It's not quite what you have above, but there was no mention of ways to clip or constrain the domain to certain coordinates.
Pgfplots
Alternatively you could reproduce the same plot using pgfplots which, apparently, is better at controlling what is displayed. For example, in your case, you could write domain=-1:4 and anything beyond those coordinates would be clipped. This is how your graph would appear:

Code (for both pictures)
\documentclass[tikz,border=2mm]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{datavisualization}
\begin{document}
\begin{tikzpicture}
\datavisualization [%
scientific axes,
y axis={min value=-2},
visualize as line,
]
data {
x, y
0, 0
1, -0.5
2, -2
3, -0.5
4, 0
};
\begin{scope}[xshift=8cm]
\begin{axis}[
height=4.7cm,
width=7cm,
xtick align=outside,
ytick align=outside,
x tick label style={font=\footnotesize},
y tick label style={font=\footnotesize},
enlargelimits=false,
ymin=-1
]
\addplot[mark=none,line width=.6pt, domain=-1:4] coordinates{(0,0) (1,-0.5) (2,-2) (3,-0.5) (4,0)};
\end{axis}
\end{scope}
\end{tikzpicture}
\end{document}