Obviously both of those cases are quite severe examples of edge damage, but even for single chips smaller than this re-grinding the bevel manually can be challenging.
This level of edge repair is generally considered a job for power grinding. It is possible manually, I've done it entirely by hand on 'rescue chisels' using a combination of diamond plates and a coarse waterstone, but it's not something you'd want to do routinely. It's a lot of work and if you're sharpening freehand because you have to stop and check for square frequently (and then adjust as needed if you're going out of square) it takes even longer than you expect.
If you do this with any frequency you'll probably want to use some kind of powered grinding/honing tool for the bulk material removal, a small bench grinder as least. It doesn't have to be an expensive grinder and it doesn't have to be a low-speed model or have a cool-cutting aftermarket wheel, although both of those are advantages. But at higher speeds using a typical aggressive wheel (often grey in colour) you will want to have a container of cold water immediately to hand to dunk the chisel tip into periodically to cool it before continuing.
Note: some sharpening gurus (e.g. Leonard Lee in his book on sharpening) say this dunking leads to microfractures that damage the steel near the tip and make it prone to chipping, however, cooling in cold water periodically during grinding is extremely common practice and most users experience no issues. Myself, I've seen no evidence of it when cooling metal cutting tools (knives, gravers and chisels in various metals) during various grinding operations. However, it is probable that the key thing here is the size of the temperature change. So dunk early and often, and after the first dunk pay attention to the drops of water on the back of the chisel — they give you a read on how the temperature is rising.
As with all grinding, don't press hard. Let the stone do the work, it should almost be the weight of the chisel against the stone pressing it home. Even doing this the tip will heat up and pauses or dunking in water may be necessary.
Your first thought might be to just work on the bevel, grinding back at that angle until the chips are gone. This is a mistake because there's a high potential for the thin edge to overheat (thin metal heats up fast). It's a bit scary but it's actually better to grind the edge 90° and straight across until you've removed the chips, then work to re-establish your desired primary bevel angle.
This way you're grinding at or near a thin edge for minimal time.
Although the chisel can be held in the fingers for both grinding operations once you get to grinding the bevel itself a jig can be a big help. Even without dunking you need to pause periodically to inspect the progress of the grind on the bevel and it can be difficult to maintain the same angle accurately, so some sort of jig is highly advisable.
This jig doesn't have to be complex or elaborate to work well:
As you can see you can knock up something that will work well from shop scrap and a few bits of inexpensive hardware.
Doing this by hand
If a powered grinding tool of any kind is not in the budget, or you simply enjoy the hard work and challenge, I'll include a basic guide to doing this manually.
- First off I would highly recommend using a coarse or extra-coarse diamond plate for the bulk removal. The difference in grinding speed of diamond is quite noticeable when doing this level of material removal.
- A coarse waterstone can be used, but it will take much longer.
- A coarse oilstone can be used, but it will take longer still.
- If doing this on a waterstone, even being conscientious about working over the entire stone, expect that you might need to re-flatten the surface after doing this amount of material removal. Most particularly with any very hard chisels with waterstones wearing quickly it's possible you may need to re-flatten once during the operation.
- Not due to the risk of overheating, again it seems like it's best to grind the tip flat across until the chips are gone and then to set to work grinding the bevel much as you would doing regular sharpening. It's hard to explain why this works better but I've tried both ways and I highly recommend it as the way to tackle this sort of major re-profiling.
- If using stones grind the edge flat on the side of the stone if possible; it's very easy to dish the face of the stone otherwise.