@jeffe,
You can use valueFormatString property to define how X-axis labels must be formatted before they appear. Please take a look at this code-snippet for an example on showing only date as the labels,
axisX:{      
   valueFormatString: "DD-MMM" ,
}, 
Kindly, take a look at this JSFiddle for an example on the same. 

—
Adithya Menon
Team CanvasJS