It is not in any way practical, and fundamentally impossible (in a reliable way), but it may be possible to some extent.
The obvious hindrance which makes the endeavour fundamentally impossible is that whatever it is you decrypt, once you've read it, it's inside your head. So, to be sure the secret stays secret, there would have to be a poison pill mechanism of sorts. Maybe a capsule that contains a TTS engine and transmits the message to you via bone conduction, and then explodes, blowing off your head.
Because, you know, as long as you breathe, you can just tell someone. Still, let's hope you don't repeat aloud what the TTS is whispering in your head.
That aside, there exist data storage systems which can be read only once. DRAM and Ferroelectric RAM as a non-volatile alternative are two examples of that. These need either an explicit write-after-read built-in, or something different (e.g. capacitator circuit). Otherwise, reading the information destroys the information. Leave that out, and you have gone forward a big step.
Now, at the very least, one would have to make two copies (one onto a non-destructive-read storage, and then another one to actually have a copy). Still, that's quite within the realm of "doable", but depending on hardware compatibility it may be somewhat of a burden anyway (not sure you can just wire up two entirely different, incompatible storage types and copy data like in Star Trek, might very well be that it proves a bit more difficult than that!). But we're not at the end.
The decryption key, and even part of, or the complete the decryption executable (assuming loops are unrolled) might as well be stored on destructive-read storage inside the decryption hardware. The decryption key does not ever need to leave the chip, so other than for "data", there need to be no lanes for transmitting it. It's read during decryption, and after that it's gone. So... there you go.
Unless you assume someone might drill holes the size of a few dozen nanometers into the chip and use nano-wires to somehow wiretap into the storage, there's no way of getting to the data. I'm not saying this is impossible, just... that it's kinda crazy. No information is valuable enough to warrant that. Plus, I'd guess it might be a quite risky procedure since accidentially leaking a tiny charge or going a few nanometers too far left or right will inevitably destroy the key, too.
As the decryption key is usually very small (32 bytes or less), it could in fact be stored inside a secure enclave processor or similar, as is done in many mobile devices routinely nowadays. That storage could also have destructive reads (and no external access to enclaved data, much like on every modern phone). But it doesn't even need to.
You could have fuses such as in Samsung's Knox or Apple's SEP, which in principle allow you to decrypt the data N times (not just exactly once, but exactly N times, as many as you like). After that, the processor simply doesn't refresh (or explicitly overwrites) the key. Or, much less secure (but probably still good enough), it only refuses to decrypt.
Thus, making a copy of the encrypted data really won't do much good because you cannot decrypt the copy.
Of course, someone can still trivially copy the decrypted data, if there are any means of doing so. Usually there are, both digital and analog. If nothing else, you can have two or three people looking at the screen simultaneously, or take a photo.
That, however, is a problem that you just fundamentally cannot solve (except by an exploding device, or a device releasing nerve gas).