The total volume of the oceans is about 1.35 billion cubic kilometers.
The total volume of the mantle is 909 billion cubic kilometers, roughly 1,000 times greater.
Moreover, the radioactive minerals which came out of the Earth's crust either originated within, or are otherwise found in, the Earth's mantle and core.
We're also talking about timecycles of hundreds of thousands of years, and, frankly, a mixing dynamic which is probably not well known.
I'm actually not much a fan of nuclear power (it's potentially useful, but highly problematic, and much more limited in capacity than is generally understood), but deep-mantle-injection would actually be, on the grand scheme of things, statistical noise so far as any radioactive risk is concerned.
We're also not aware of any biological activity occurring within the mantle. The problems with ocean pollution -- plastics, metals, fertilisers, etc. -- were that these are:
1. Generally unevenly distributed, with concentrations in specific areas.
2. Highly interactive with life forms -- biological concentration of heavy metals, forming algael blooms, etc.
3. For lighter detritus (especially plastics), confined to what's effectively a film at the surface of the oceans, rather than mixed throughout the full volume of the ocean.
Even for substances which do mix with seawater, such as CO2, the rate of mixing through the entire benthic column is a concern.
Where radioactive waste has entered seawater (numerous reactor cores, mostly from the nine nuclear-powered submarines which have sunk, waste disposal, and liquid discharge e.g., from Daichi-Fukushima), dilution with seawater tends to make this a very low-level threat at any distance from the immediate site.
(Despite this, I strongly discourage the practice.)
My point: in the list of risks to worry about, this isn't one I'd spend much time on. I've already spent more than it's worth.
