Start with what the express clause is for, because the intuitive reason is the wrong one. People generally imagine a disinheritance clause as a precaution against a will being ignored. It is better understood as a provision that operates in the gap: intestacy rules apply to any part of an estate a will does not dispose of, and a will can be silent about a person and still leave property passing to them by default. The express clause reaches that default. It says the person takes nothing even from what the will fails to dispose of, which is a narrower and more useful job than the dramatic reading suggests.
Then read the second half of the same sentence, because it changes the outcome. The excluded share does not simply go to the others. It "passes as if that individual . . . had disclaimed an intestate share," which sends the question into the state's disclaimer rules. Minnesota's section 524.2-1108(d)(1) provides that a disclaimed interest passes as if the disclaimant had died immediately before the interest was created, and then adds the sentence that matters here: "if, by law or under the governing instrument, the descendants of the disclaimant would share in the disclaimed interest by any method of representation had the disclaimant died before the time of distribution, the disclaimed interest passes only to the descendants of the disclaimant who survive the time of distribution."
Read together, those two provisions raise an obvious question about whether excluding a child sends that child's share to the child's own children, which is frequently the opposite of what was intended. The statute answers the drafting problem in its own words without anyone needing to resolve the question: it permits excluding "an individual or class." A clause naming the person and their descendants as a class does not leave the routing to be argued about later. This is the single most useful thing on this page, and it costs one extra phrase in a document.
The ceilings come from elsewhere, and the spouse's is the hard one. A surviving spouse generally cannot be excluded outright, because most states give them a statutory claim that overrides the will. Utah's version is a right of election "to take an elective-share amount equal to the value of 1/3 of the augmented estate," with a supplemental floor of $75,000 where the ordinary computation falls short, and with homestead allowance, exempt property and family allowance charged against rather than added to it. The word doing the work is "augmented": the pool is deliberately larger than the probate estate, which is why routing everything through beneficiary designations is not an answer to it. The live Family and Life Events guide covers the elective share and the marriage-after-the-will problem in detail, and published marital property covers the state systems; neither is restated here.
The child's protection is narrower than its reputation, and it has exceptions the general accounts omit. Minnesota's omitted-children section, 524.2-302, reaches only "the testator's children born or adopted after the execution of the will." Where the testator already had living children when the will was signed and left them property, the omitted child's share is limited to those devises, computed as an equal share among all the children, and the earlier children's devises "abate ratably," with the court preserving the testamentary plan as far as possible. So the protection is usually a redistribution among the children rather than new money, which the Family and Life Events guide already tells readers.
What that guide does not carry is subsection (b), and it is the operative provision for anyone contemplating an express clause. The protection does not apply at all if "it appears from the will that the omission was intentional," or if the testator provided for the child by a transfer outside the will and the intent that it be in lieu of a testamentary provision "is shown by the testator's statements or is reasonably inferred from the amount of the transfer or other evidence." The first of those is the whole point of writing the clause: in Minnesota, a will that says plainly that a child is being left out is a will the omitted-child statute does not reach. Subsection (c) handles the odd case where the omission happened only because the testator believed the child was dead, giving that child an intestate share, and (d) lets the issue of a deceased omitted child take in their place.
Two things a disinheritance clause does not touch at all. It does not reach a retirement account, a life insurance policy or a bank account with a beneficiary named on it, because those pay whoever is on the form and never enter the estate. It does not reach property held with a right of survivorship. Between them those channels hold most of what a typical household owns, so a plan that puts real effort into the will and none into the paperwork can produce exactly the result the will was written to prevent. And a clause excluding someone does not stop them going to court: it removes what they would take by default, which is a different question from whether they can attack the document, covered on the will contest page.