You can add trim left to tikzpicture:

\documentclass[a4paper,oneside]{article}
\usepackage{tikz}
\usepackage{blindtext}

\begin{document}
\blindtext

\begin{figure}[h!]
\makebox[0pt][l]{\begin{tikzpicture}[y=0.5mm, x=0.333\textwidth,trim left]

\def\axissep{5mm}
\def\tickl{2mm}
\def\xlabsep{3mm}

% y-axis
\draw (-\axissep,0) -- (-\axissep,100);
% y-ticks
\foreach \x in {10,20,30,40,60,70,80,90} % avoids double inking on 0, 50 and 100 that becomes thicker
    \draw (-\axissep,\x) -- ++ (-\tickl,0);
% y-tickslabels
\foreach \x in {0,50,100}
    \draw (-\axissep,\x) -- ++ (-\tickl*2,0);
\foreach \x in {0,50,100}
    \node[anchor=east] at (-\axissep-\tickl*2,\x) {\x};

% x-axis
\draw (0,-\axissep) -- ++ (3,0);
\foreach \x in {0,1,...,3}
    \draw (\x,-\axissep) -- ++ (0,-\tickl);

% x-labels
\node[below] at (0,-\axissep-\tickl){1};
\node[below] at (1,-\axissep-\tickl){2};
\node[below] at (2,-\axissep-\tickl){3};
\node[below,align=center] at (3,-\axissep-\tickl){4};

% grid
\foreach \x in {0,10,...,100}
    \draw[very thin, color=gray] (0,\x) -- (3,\x);

\draw (0,10) -- (1,14) --(2,45) -- (3,23) ++ (1mm,0) node[anchor=west] {\tiny Some label};

\end{tikzpicture}}
\end{figure}

\blindtext

\end{document}


I also placed the tikzpicture inside a \makebox of 0pt width to prevent the overfull bad box and changed the incorrect onesided to oneside (though that is the default for article).



Align tikzpicture to body text with node as reference
As a follow up to this etymology question, does "so far, so good" carry a negative connotation?

For example, after having her sonogram, my wife asked the technician if everything was okay.  The technician replied, "so far, so good."  My wife later remarked that she didn't like that the technician used the phrase because it sounded like things will be going wrong later.

I always thought this phrase was positive and that it was a replacement for the word "good."
