Do you know which sort of hydrangea? In theory mopheads and lacecaps can be cut hard back in early spring but if they have been neglected and not cut back each year they may not regenerate so well.
H. paniculata is cut back each year to strong buds on the previous year's wood.

When my sister passed away two years ago, she had a monster hydrangea in a border which I cut right down to the ground ready to remove it. This was in the Spring. I then didn't get round to sorting the garden until the following Spring when it had put on huge amounts of growth and even one flower head. You might upset it for a while but do it when the weather improves in a few months.

You can renew mopheads less drastically by cutting some stems right back this year and the rest the following year. Not necessarily completely to ground level though as often the new growth appears from a bud on the old wood.