So, I have a model, 850 vertices, ~1600 faces. The problem is, after converting it to md3, the exporter auto smoothes the faces causing two issues.

The first one is, this doubles the vertex count (vertices get automatically separated) and ET doesn't want to work with a model that has more than 1025 vertices per segment.
The second problem is, a great portion of the model is supposed to have hard edges and this makes the shading look blurred.

Since the limitation isn't per model, I can split it up into more segments which are under 1025v limit. The thing is, that doesn't really make sense since I don't want to use smooth shading at all.

I've tried exporting with blender, making sure that all faces were "set solid" (as opposed to set smooth).
Also with Misfit Model 3D, I start up with a 850V model and as soon as it's saved as .md3, the vertice count jumps to 1700, even though it's smoothing setting is set to 0.
Lastly, in Milkshape, smoothing groups aren't used and auto smooth is off, the problem remains.

When the model is exported to .ase or .obj, there are no problems. Is this the feature of .md3? Auto smoothed faces?

Just break your model up into more pieces. Done.

I've never had problems with smothing in MD3, so I dunno what is the problem.

You need to remember something, the .md3 exporter recalculates the normals of your models, doubling the verts. The only way around it is to break up your model into lots of small pieces.