We need to cut off old, rotten deck joists flush to the side of the house. How?

[OnionPatch]

We're repainting the house so it's time to replace that deck but it was built on joists that extend out from the actual interior of the house, not attached to a ledger. The ends of the deck joists are rotten but not the parts of them against the wall of the house, so we'd like to cut them off flush and bolt a ledger for a new deck to the ends. We have quite a few saws here in our workshop, but nothing that can cut along a flat surface like that. The hubbie is thinking there may be no such thing. Is that true? I keep wishing (perhaps futility) that there was some specialized saw we could rent somewhere that will saw these off flush like the red line I drew on the pic. If we can't do that, then how do we attach a ledger? The joists start to be rotton in places about halfway out, so we don't want to use them.

We kind of need a replacement deck here or we're going to have a big, sliding glass door to nowhere.

Advice, anyone? (PS Excuse me if I'm not using the correct terminology, I'm pretty new to this kind of thing.)