The following is a thought experiment about what would happen if we were to totally remove the elements of the periodic table from the human body, one by one. Since the results would be obvious, immediate, fatal, and explosive if we started from the top of the table, with hydrogen, we will instead remove them from the bottom of the table, starting with uranium, the last "naturally occurring" element. We will remove the elements at one minute intervals from our hypothetical test subject. And remember kids: don't try this at home.
We start at T=0 with uranium, which is both present in only tiny amounts, and is also not necessary for biological functioning. Since uranium is radioactive, we might be doing ourselves a favor to remove it. Or perhaps not: if someone had to live a lifetime with no radioactivity in their body, it might have bad unforeseen effects, as perhaps background radiation is necessary to cleanse our body of parasites. But in the scale of minutes we are working in, that is not a factor. The next few elements are all radioactive and not a factor in our biology. At T=9, almost ten minutes have gone by, and our subject would not even be aware of the macabre experiment they find themselves in. This is where we hit the first stable element, bismuth. Although stable, bismuth is not present in our bodies in appreciable amounts. The next three elements, lead, thallium and mercury, are, in small quantities. Removing them will be beneficial to our health, but we won't really have time to undo a lifetime of low-level brain damage, so their disappearance goes unnoticed. As does the removal of gold, platinum and irridium a few minutes later. (Unless you have a filling, which we may or may not be considering in this thought experiment). A little while later, we encounter the rare earth elements, or lathanides, and again, we are dealing with elements that have no known role in our metabolism.
At T=34, over a half hour into our experiment, and having removed one-third of the periodic table, our subject would not have noticed anything, and unless we had geiger counters and magnetometers pointed at them, neither have we. The total weight of all the elements that have gone missing is probably in the milligram range. The next two elements, barium and cesium, might be noticed in their absence. They are still present in only very small quantities, and they are not necessary for life, but, they do mimic the effect of other, vital elements. They are two periods (rows) below calcium and potassium, respectively. They probably carry electrical signals in nerves like those elements do. As they disappear, our subject might feel minor CNS effects, but even that is questionable. At T=38, we reach the first element that we know is needed for life: iodine, which is present in several related hormones that regulate thyroid function. Along with that role, iodine is also present as an ion, and losing it might have the same effect as losing barium and cesium did. While we know that iodine is needed for life, its disappearance would not cause immediate problems.
After our first notable minute, things would quiet down for the next ten minutes. Most of the elements disappearing are either toxic, like cadmium, or neutral, like silver. Although silver may play a small role in human metabolism, it wouldn't be noticed, especially compared to what is coming. 49 minutes in, the molybdenum disappears. Molybdenum is also necessary for life, as a cofactor in several enzymes, but its absence would not be immediately obvious. We still have probably not noticed anything overt. Five minutes later, we come to two more elements that would be noticed: strontium and rubidnium. These elements are above barium and cesium, and they also are basically treated by the body as identical to potassium and calcium, but because they resemble them more, even more so. Also, they are present in larger quantities. Since strontium plays the same role in the skeleton as calcium, there might even be some physical changes to the skeleton's structure. However, it still might barely be noticed. As would the disappearance of bromine, which takes the role of chlorine. Selenium, too, while present in a few enzymes, would not be immediately missed.
So far, all these elements together might weigh in the gram range. Perhaps them all disappearing at once would disrupt the body's ionic balance, but for the most part, nothing has left that has to do with our bodies immediate metabolic processes.
We are now reaching a run of elements that are necessary for human function. At T=61, a little over an hour in, we hit zinc, which is necessary for human life, then copper, which also is, nickel, which is probably not, and cobalt, which is. Probably losing all of these at once, together with the elements that have already been lost, would be noticeable. But it is not worth too much debate, because the next minute, the result is clear.
At T=66, all the iron disappears from our subjects body. Since iron is used to transport oxygen, our subject can no longer breathe. It is true that some oxygen can diffuse into and out of the blood without the iron-containing heme protein, but it would not be enough to live off of. I also imagine that iron's general ubiquity in the body and in other proteins would mean that without it, many different body functions would shut down at once. I doubt that consciousness would be maintained after this point. Which is probably for the best, because after 5 minutes of relatively unimportant elements (like vanadium) vanishing, all the calcium disappears. The skeleton collapses, the nervous system can't function, and the heart can't contract. Individual cells might still carry on life, but the organization and the structure of the body is gone.
A few minutes later, even that cellular metabolism ceases when the phosphorus is taken away. Several other elements, like sulfur, chlorine and magnesium on this row, are also vital, but at this point, it doesn't matter.
The next thing that really matters happens at T=85, when the oxygen disappears. This includes the oxygen in the body's water, meaning that all the hydrogen in the body would suddenly be free, and it would probably explode. At this point, the structure of the body disappears. An hour and a half into the experiment, and the subject is gone.
This is, obviously, a thought experiment, for reasons both technical and ethical. However, it reveals interesting facts about the human body. If someone removed all but five elements from a human body (hydrogen, oxygen, carbon, nitrogen and calcium), it would still structurally look the same (until you noticed the blood was colorless). Half a baker's dozen other elements provide the minute to minute functioning of metabolism (sodium, phosphorus, calcium, potassium, sulfur, chlorine and iron), while another ten or so elements are necessary for longer term metabolism (hours to weeks): copper, zinc, magnesium, cobalt, molybdenum, iodine, and selenium. Without the first group, you have no body at all. Without the second group, you don't have life, and without the third, life will spin down fairly quickly. But out of the entire periodic table, large numbers of elements could disappear without ill-effect, and perhaps without being noticed at all.