If you have a good-sized electric drill, tighten the chuck around the bolt and try to back them out with power.
Casey

I would grind them off, you can get closer than sawing.

It looks like the bolts are in an anchor---if that is spinning, there is little hope of getting the bolt removed.

You might try using a hammer to hit the bolts sideways/up/down/at all angles to loosen it in the brick. If that works, fill the holes with patching compound, smooth and paint.

If that does not work, cut them off and grind them flush with the brick and patch.

I'd bet what you have is one of these:
{{!gwi}}

They don't come out very easily. As Handymac suggested, you can try tapping them which may break enough of the brick to loosen the anchor.

Frankly, it would be easier to grind them off and patch.

Cut them off and patch.

There is no way to remove them without damaging the wall (as in making a larger hole, often with a diamond coring bit).

try tapping the end toward the block there may enough depth in the drilled hole to loosen it.

"try tapping the end toward the block there may enough depth in the drilled hole to loosen it."

The anchored end is larger than the hole used to insert the bolt.

Cut them off and patch.

Thank you so much for the suggestions, everyone! I had someone doing exterior painting for me today and I had him come in and take a look. He just hammered at them until they snapped off and then banged the rest back into the brick. Now I just have to patch up the holes. So happy to have that resovled!

There are few things in life that can't be fixed with a big hammer.