This looks like alternaria leaf spot, a fungal disease caused by the pathogen Alternaria spp. It can be a problem when plants are watered overhead and the leaves get wet, or in seasons with frequent rain. 

To manage the disease, always water at the base of the plant and keep leaves dry. Provide one inch of water per week to help alleviate the stress on the hydrangea. Clean up fallen leaves and dispose of them with the trash do not compost the diseased leaves. If there are just a few leaves with spots, clip them off to keep the healthy leaves from being exposed. Clean your tools with a bleach solution to keep the fungus from spreading to other plants. Place clean mulch around the base of the plant to prevent soil from splashing onto the plant during rainfall. Keep mulch pulled back from around the plant stems so it doesn’t touch the plant stems.

Using a fungicide spray according to label directions can protect fresh leaves. This is a recommendation from Extension:

“Products containing chlorothalonil, myclobutanil or thiophanate-methyl are most effective when applied prior to or at the first sign of leaf spots. These fungicides work best to protect newly developing leaves, but they will not protect new growth that emerges after the application has been made. Consequently, to keep plants relatively free of the disease, multiple applications (usually every 10 to 14 days) may be necessary.

Remember with all pesticides, always read, and follow the label directions. Complete coverage of the leaves with the fungicide in conjunction with proper timing of applications is important for successful leaf spot management.”

More details here: Hydrangea Diseases (psu.edu)

Foliar diseases of Hydrangea FBG 022916 G1.pdf (tnstate.edu)

I hope this information helps and have a great gardening summer.

I would not cut the plant down to a few inches. I would prune off the worst of the branches but no more than one third of the branches on the hydrangea plant. This will help increase air flow around the plant. Continue to provide one inch of water a week at the base of the plant to avoid wetting the leaves. When the leaves drop in the fall clean everything up and dispose of the plant debris. See how the plant looks next spring and if necessary, use a fungicide on the hydrangea.