Split is probably the easiest way to do what you want. I think it's pretty straightforward, but I'll include a couple of screenshots for clarity. It sounded like you didn't have any trouble getting the workplane put in correctly, so I won't cover that.
Make sure to select the correct method. The one I have selected will delete everything in the direction of the arrow. The other method is a little more complex and would allow you to keep the other side and split the part into two. It doesn't sound like this is what you wanted.
The part after the operation. The split is considered a feature, so editing and suppressing it is easy.
I use this a lot in a class that requires designing cast parts. As a cast part has two states- when it comes out of the mold and after machining, you have to supply drawings a models for both states. This is just one way to quickly switch between two states of a part with out getting into complex spreadsheets to drive parameters. It's also considered a little more acceptable then cutting with extrusions, something which was almost never acceptable on a class project.
There is almost always a dozen ways to get something done in Inventor. This is just the one that I would use knowing nothing else about it. Replace face is another good method.
Also, you should be able to place a sketch on the workplane, and cut/extrude from that sketch. The direction of travel should be 90 degrees from that sketch, and not from the origin planes. I don't know why that wouldn't be working for you.
-Andy A.
And yes, the date and time on my computer are correct. What better to do at this time of the morning then play around with Inventor?