How did you divide it? You can't separate the roots--it just doesn't work. Taking cuttings from the growing tips does, and does not harm the plant. I have had the same hanging geraniums for about 10 years. Not the same plant but cuttings from them.

In any case I don't think your problem was the cuttings, but the soil you had the plant in. Your geranium had leaf spot disease. Your cutting may be infected too so mix up a solution of 1 teaspoon of baking soda and 1 quart of water add a drop of hand soap--just 1 drop. Too much soap will burn the leaves, but you need it to make the soda stick. Baking soda is a fungicide. Put this in a spray bottle, shake and spray the rooted cutting every 4 days until you are sure it is not infected.

Whenever you take cuttings from any peli it is important to have everything as clean as possible. Cleanliness goes a long way towards preventing blackleg, and the success of the cuttings and plant

Good luck

Tan or brown spots on the back side or bottom of Ivy Geranium leaves is quite often oedema. It is a condition caused by the plant being a little too damp. Basically, an Ivy Geranium cannot transpire fast enough, becuase of the glossy texture of the leaves and the cells get so full of water that they burst. It is kind of unsightly, but will not hurt the plant, except in extreme cases where it can damage both sides of the leaf. Let the plant dry out or take new cuttings and you should be just fine, if it is indeed oedema.