No, that is not exactly the way it works but I see why you are confused. A Big Leaf Hydrangea (h. macrophylla) like yours already has developed a dormant, spring 2024 flower bud at the end of most stems. That happens every year and they typically do that anywhere from July-September 2023, depending on the geographical location. That flower bud at the end of the stem normally opens in spring 2024 and resembles tiny broccoli heads. In addition to that flower bud, the stem also develops back up, dormant, spring 2024 flower buds lower down the stem but, these buds only activate/bloom if the bud at the end of the stem is killed by weather/deer/pests or when the stem end is either prematurely pruned or pruned incorrectly. Thus, trimming the stems down to the height of your knees could now result in no or in few blooms in 2024 if you prune "too low".
Pruning: For Big Leaf Hydrangeas, use pruning only to control shrub size and be aware that if done improperly, it may result in no blooms in some years. If you were to prune a stem below the last back up flower bud of a stem now, that stem will be unable to bloom in spring 2024. But if you prune that stem somewhere above the last/lowest back up flower bud, you will probably get a bloom in spring.
To avoid pruning/blooming issues, this species of hydrangea should be planted where it can attain its estimated size at maturity per the plant label and then it should be rarely pruned. Why? Because the stems spend most of the year developing flower buds, carrying the dormant flower buds until spring and finally... blooming. Unfortunately, these flower buds are not always visible but are inside the stem. Get the pruning timing wrong and that might result in no blooms or very few blooms during the next year.
Leafless stems: In the spring, the shrub breaks dormancy in two phases. First, it develops brand new stems from the crown or base of the stems in spring. Several months later, the leafless stems that have the dormant spring blooms leaf out and bloom. Leafless stems can be pruned all the way down only if they still remain leafless by the end of May in the south, the end of June in the north, in July near Canada or by the end of the astronomical spring elsewhere (not sure where you are located).
Deadheading: Deadheading removes blooms only. It is not used to control stem/shrub size. It is used to remove blooms (usually browned out blooms) or to get some blooms for drying arrangements. To deadhead correctly, cut above the very first pair of leaves; but if the stem is leafless, cut the string that attaches the bloom to the stem instead. Deadheading like that normally does not impact future blooming.
Old wood versus new: This year's stems are referred to as old wood in 2024. All things being equal, a bloom will open in the spring from this year's stems and it will resemble tiny broccoli heads.
Stems that begin to grow from the crown or base of stems in spring 2024 are referred to as the new wood in 2024. These stems can start to bloom by late summer/fall 2024 if this variety is remontant ('rebloomer' in advertising jargon); otherwise, they will start to bloom in spring 2025.
Smooth Hydrangeas (h. arborescens) or Panicle Hydrangeas (h. paniculata) can be safely pruned in the way that you are pruning the Big Leaf Hydrangea now or you can elect not to prune the stems either (let the blooms fall). These hydrangeas typically do not require pruning when young and they develop flower buds in mid spring or summer; then their flower buds immediately open. Thus, these two types of hydrangeas should typically not be pruned from mid-spring through summer. Deadheading of their blooms can be done at any time of the year or never. These types of hydrangeas suffer from flopping issues by the end of the summer or so. It is best not to prune them all the way down on a regular basis as green or thin stems promote flopping if they carry a bloom.
For size control: Methods used to control shrub size include pruning and rejuvenation pruning. The timing of pruning can be difficult to get right but you can usually safely prune after the shrub stops opening new flower buds in spring/summer but before the plant develops new dormant, spring flower buds at the ends of the stems. These buds may not always be visible at first so, once the opening of new blooms stops, assume you have just a few weeks before flower bud development starts. Prune within those few weeks. This is the same blooming process that azaleas/rhododendrons/etc. go through. In addition to pruning, you can also control the shrub size using rejuvenation pruning. Note that you should not need to do either of these two methods often/annually. If you do, the shrub is planted where it cannot attain its estimated height/width plant dimensions so consider transplanting it elsewhere.
Going forward: if you wish to deadhead the blooms at the end of the stems, cut above the first pair of leaves or, if leafless (all stems appear leafless in the pics) then cut the string that attaches each bloom to its stem.
Winter protection: in some areas with either very cold temperatures or with wildly fluctuating temperatures, the leafless stems typically die and never leaf out. When this occurs reliably, you get no blooms, there is no leaf out by the leafless stems, all new spring growth originates from new stems and thus, further action is required to ensure spring blooming. To get reliable spring blooming, use winter protection so the stems and their flower buds survive cold temperatures, late frosts and wildly fluctuating temperatures (you can see videos in Youtube by searching for 'hydrangea winter protection'). Or you can grow these shrubs in containers but move them to the garage/basement from your city's average date of first frost through your average date of last frost.
