Rather than removing it, I would suggest covering it properly with greenhouse film (translucent plastic, UV-protected with typically 4 year guaranteed lifespan, typically 11-13 cents per square foot) rather than a blue tarp. With proper edge attachments it will be much more secure and weather tight, and far less unsightly as well.
You could also use (at greater cost) a twin-wall (like corrugated cardboard) rigid plastic sheet greenhouse glazing, which is available in polycarbonate or acrylic, and is much more difficult to break than glass. It looks suspiciously like your roof dumps stuff on the greenhouse roof, which is poor planning for the life of the greenhouse roof (particularly in glass) if ice falls from the house roof.
Both of the above approaches would be best served by removing at least all the broken glass, or all the glass, period. That would also be the first step in removing it, period.
Finally, you could repair the broken glass with new glass. But if the roof above dumps ice on this one, that won't be a satisfying solution.
With any of the above you could also repoint/repair the brick.
Your pictures are a bit vague, but if the "sliding glass doors" are down a set of steps from the greenhouse floor level you could simply remove the thing and place a normal basement bulkhead door over the stairs and doorway. Typically made of steel, those will take a pretty large ice impact in stride.