I have never found any home remedy that worked on my clematis. Best to be proactive and spray before the problem shows itself with a fungicide.

There's no reason why a home recipe for powdery mildew shouldn't work, but Miguel is entirely correct - you need to be proactive. The nature of fungal organisms is that you can't "cure" them or remove them once they are evident but you can prevent their development or their spread to non-infected foliage. So the time to treat for powdery mildew is before you see signs of it. Tricky I know, but at least you'll be prepared for next season - now your only solution is to cut it back hard.

There are quite a few home remedies that are effective on powdery mildew. The Cornell formula (developed and field tested by Cornell University) is one of the oldest and still very popular: 2 Tbsp ultrafine horticultural oil (salad oil is a valid substitute) and 4 Tsp baking soda to a gallon of water. You can add a few drops of dish soap to help keep the mixture emulsified. Milk is also an effective fungicide - just mix at a 50-50 dilution with water. My preference is Neem oil, a naturally occurring biocontrol extracted from the neem tree. If you grow roses, you may be familiar with Neem oil from a product known as Rose Defense (manufactured by Green Light), which is an extremely effective and organic insecticide, miticide and fungicide.

But for best control, these must be applied (and repeatedly) early in the season before you see signs of the disease. Cultural controls can also help - provide good air circulation (you may need to thin out very lush vines), keep the base clean of weeds and any debris and water deeply at the roots, avoiding overhead watering, and focus on those plants or vines that are less prone to the problem. But if you live in an area with high summer humidity, PM may just be a given and very hard to avoid.

Gardengal is right. Fungicides don't kill fungus. They protect new growth from getting it. Cutting the vine down then spraying the new growth is the way to go.