How do you describe blind people and dumb people in Japanese?

There really seems to be no direct word for blind and dumb people. Because the Japanese think it would be impolite to call disabled people this way.

We call the blind "目の不自由な人（目が見えない人）" and call "口がきけない人（しゃべれない人）"　the dumb.

The dumb:

✕「唖 」（おし）

〇「発話障害」（はつわしょうがい）

 ✓「口がきけない人」

The blind:

✕「盲人」（もうじん）

〇「視覚障害者」（しかくしょうがいしゃ）

 ✓「目の不自由な人」

The deaf:

✕「聾」（つんぼ）

 ✓「耳の不自由な人」

Japan usually uses organ + "の不自由" to indicate that this organ is not functioning correctly.

They don't use the word "障害" very much, although it is correct.