It’s amazing how contrived and detached from reality the counterexamples for utilitarianism have to be able to attack even the most basic forms of it. It really makes you think that utilitarianism is a solid principle.
This also deliberately avoids introducing irrelevant arguments. By framing it as a mugger who wants to gain money for purely selfish reasons, we deliberately exclude complicating factors from the statement.
* The argument could be framed around donating to the Susan G. Komen Foundation, rather than a mugger. With the controversies it has had [0], it could be argued that these donations may or may not increase total utility, but donations to charities are part of the best possible path. However, using the Susan G. Komen Foundation as an example relies on accepting a premise that it isn't using donations appropriately, and makes the argument dependent on whether that is or isn't the case.
* The argument could be framed around allowing tax exemptions for all self-described charitable foundations, with Stichting INGKA Foundation [1], part of the corporate structure that owns IKEA, playing the narrative role of the mugger. The argument would be that the tax exemptions provided to charitable foundations are necessary for bringing about the best outcomes, but that they can be taken advantage of. Here, the argument would depend on whether you view the corporate structure of INGKA as a legitimate charity.
* Even staying with purely hypothetical answers, we could ask if the mugger going to starve should be mugging be unsuccessful. These could veer into questions of the local economy, food production, and so on, none of which help to test the validity of utilitarianism.
I've heard this described as crafting the least convenient world. That is, whenever there's a question about the hypothetical scenario that would let you avoid an edge case in a theory, update the hypothetical scenario to be the least convenient option. What if the mugger just needs a hug? Nope, too convenient. What if the mugger isn't going to go through with the finger-chopping? Nope, too convenient.
[0] https://en.wikipedia.org/wiki/Susan_G._Komen_for_the_Cure#Co...
[1] https://en.wikipedia.org/wiki/Stichting_INGKA_Foundation