As mpowell said, a waterjet can cut titanium; in fact it can do it very effectively with no heat affected zone. However, how quickly depends on several variables.

First, how thick is the titanium? The thicker a material is, the longer it takes any machine tool to cut it.

Second, how much water pressure is being used? A Flow 87K Hyperjet could cut up to twice as fast as a 60K or 55K machine.

Third, what size orifice is being used? Generally a larger stream equates to faster cutting.

Fourth, what type and size of abrasive and how many lbs/min are being used?  An HPX abrasive has sharper edges and is generally more aggressive.  Like sandpaper, the grit size can determine how quickly material is eroded; up to a point, more abrasive can mean faster cutting.  However, cutting with higher pressure can increase the effectiveness and end up using less abrasive.

Fifth, what size mixing tube is being used?  Again, a larger stream can normally cut faster and can handle more abrasive effectively.

Sixth, what cut quality are you looking for?  The nicer you want the edge, the slower you need to go.  However, using a Dynamic Waterjet® can allow you to cut faster and still get a good quality cut.

Lastly, what shape/contour is being cut?  As a waterjet cuts, the stream lags behind the cutting head (much like if you spray your garden hose and move your hand in a large circle), so when going into corners or curves, the jet may need to slow down for an accurate and consistent cut.  So the more intricate the contour, the longer it will most likely take to cut.

These are simply generalized statements and are not all inclusive.  The key is getting a controller system, such as FlowCUT®, that will automatically take all these (and other) variables into account to produce the desired part.