Fiddled with it a bit and here are my findings.
There isn't a way to render a scene from a different camera angle in the same frame. If we could there is probably a way to calculate where we'd position the camera from the mirror. The second issue is the drawingCanvas doesn't work with 3d meshes since they have no zbuffer and it doesn't seem to transform 3d relative to itself. We could render one frame from the mirror, save that with canvasSnapshot, and render the next from the game camera, but that is slow and would flicker annoyingly.
What we can do is duplicate the objects and position them in mirrored locations behind the mirror. We'd want the duplicate objects to only be visible in the mirror so one idea is to have the duplicate objects on a layer with force own texture and have a mask sprite over the shape of the mirror to limit drawing to that area. If all the duplicate objects are behind the mirror this should work fairly well. It will be a problem if any part of the objects are in front of the mirror since the masking will fail then. We can improve that by not duplicating objects that aren't in front of the mirror or culling by a view frustum through the mirror. Still to better fix it we'll need to clip the individual polygons by the mirror, but this requires all your meshes to be done with a distorted sprite per polygon.
The masking sounds like it should work, and does in the simple mirrored floor case, but I'm curious if we may run into issues with wall mirrors or something.
Anyways here's a semi-simple floor mirroring test by duplicating things.
dropbox.com/scl/fi/tg6b00a8oeaiuwaaw7i5u/floor_mirror.c3p