DynaBolt sleeves can be notoriously hard to remove. I'd suggest trying to drill out the bolt to begin with.
Choose a cobalt drill bit a millimetre smaller than the sleeve and drill at a slow speed. You should be able to drill through the bolt, and it will significantly weaken the wall of the sleeve. You can then crumple the sleeve into itself with a hammer and flat-head screwdriver, allowing you to pull it out.
To crumple the sleeve, work your way around the perimeter with the flat-head screwdriver. Strike blows directed towards the centre of the sleeve, folding it in on itself. - MitchellMc
Before resorting to the drilling, since that could be a messy way to go, I would first try:
1. Spraying the internals with WD-40 or similar, to start loosening the rust and its attachment to the (previously) movable parts. Then after an hour or so...
2. Using a strong bolt or any rod that will fit into the hole as a punch to hammer the broken bolt and nut back down into the hole. If they will go back, this should allow the casing to close in again and release its grip on the brick work.
At this point, if you have any Easy Outs, screw in the largest one that fits, or use any other large screw or bolt that will grab the sides and give you something to lever the casing outward with.
Another way to pull it out (if you have managed to drive the nuts back in and released the casing's grip) is to crush opposite sides of the cylinder inward using a large screwdriver to form a sort of tongue and then grab that with some narrow-nosed snap-lock pliers - or any other pliers that will grab it.
I love snap-lock pliers because you can usually get the edge of a lever between them and the surface, and then lever the pliers along with whatever they’re attached to, out. They will hopefully also allow you to twist the casing to loosen its grip in the hole.
If you can't drive the internals back in, then drilling may be the next option. - TedBear
I pretty much use the same method TedBear uses. Spray/soak it really with WD40, and once it has soaked in use a bolt that is slightly smaller than your DynaBolt. Tap the centre bolt back down into the hole. Using a flat-head screwdriver gently tap the DynaBolt sleeve to loosen it from the wall. Grab a pair of heavy duty long nose pliers and grab the DynaBolt sleeve. Slowly turn the sleeve in a clockwise then counterclockwise direction. Our objective is to tear and shear the sleeve. Once you have the majority of the sleeve out you can then attempt to pull the center bolt of the DynaBolt out.
Just to be clear, you want all the of the DynaBolt sleeve out of the wall before trying to get the centre bolt out. It is a long process so take your time. DynaBolts tend to really anchor themselves and become a nuisance to take out. Take care and be safe. - redracer01
I used a core drill on the DynaBolts which worked fine. It was fairly easy to avoid the sheath around the bolt, which is pretty soft anyway, I think. I only needed to drill in about 20mm as that was enough to get the sheath out and then the bolt. Just tap the bolt in to allow the sheath to come out. The hole is the same size no matter how deep you drill so you may as well give it a solid go as the scar will be the same.
After I removed the remainder of the bolts, the deeper rusty DynaBolt bits broke up with a sawn-off slotted screw driver. I will just fill the holes. Not pretty, but at least the bricks won’t get broken up any more. - Russ42