A more involved solution if this fits your situation and you don't mind the extra work is to use Linear Referencing tools.
Basically what you'd need to do is create a route from the desired line features and specify the end you want to start 'measuring' from. Then you could create points along the route at the designated interval....I think you'll need an input table, easy enough to create. ....those 2 tools are in the Linear Referencing toolbox, I think Create Routes and Make Route Event.... (I'm relying on memory here.)
Once you have the the points, it's an easy matter of splitting the line at the point intersections...there's a separate tool for that.
That should give you more precisely what you ask, hope that helps.
Wayne