Set minPointLength, then the zero values into null.
You can try doing a different scale of the yAxis or using the
'logarithmic' type. See updated fiddle.
Note that this does not work in all cases. The HighCharts user voice site has been asking for scale-break capabilities for a while now.
You can also set
minPointLength for series: http://jsfiddle.net/V6fvX/2/
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