Fidel,
This is something you can control with the select by location options. You don't necessarily want to get rid of the portion of the parcels that are more than 250m away from the creek, you want to be able to identify the parcel (and parcel owners) that need to be contacted about the spill. It doesn't matter if parts of the parcels extent beyond the buffer, only that you are selecting appropriate parcels for contacting by the EMS team.
To answer your question though, you could do a Clip on the parcels using the buffer as a cookie cutter. This will preserve all the parcel areas inside the buffer and delete the portions of the parcels outside the buffer. But again, this isn't what you want to do in this case. We want to identify parcels that need contacting and by clipping them, you are not representing the true shape of the parcel.
Work with the Select by Location tool and experiment with different "selection method" options. Remember than when you run this tool, all it is doing is creating a set of selected features. If you don't like the results or want to see a different selection, simply undo the selection (clear selected features) and try again.