1. Both 偷工减料 and "cutting corners" can be serious and not so serious
Does 偷工减料 have a much more negative connotation than "cut corners"?
Both 偷工减料 in Chinese and "cutting corners" in English (e.g., 1, 2, 3, 4, 5, 6, 7) can be serious depending on context, and carries the implication that it could result in death or other disasters. (E.g. "that surgeon cuts corners on hygiene" or "we don't cut corners on safety".) For example:
Corner-cutting causes worker death; which safety production-method regulation [should I] use?
Both can also refer to less serious things, e.g.:
Since there are many painting processes and it takes a long time, it's easy to cut corners; today [we] look at common corner-cutting painting-process behavior [which] should give rise to future attention.
2. How is 偷工减料 described?
Let's now look at Baidu Baike's description of this Chinese idiom:
Originally it indicated [a] merchant for profiteering secretly reduced [the] good's quality, and reduced materials. Now it also indicates doing this to save trouble; sloppy and half-hearted.
偷工减料, Baidu Baike
So 偷工减料 indeed overlaps heavily with "cut corners", with both emphasizing a reduction in quality. Moreover, multiple examples on YouDao translate "cut corners" to 偷工减料 (as does Google Translate). In a lot of cases, therefore, it's going to be a reasonable translation in at least some contexts. However, the CC-CEDICT translation is
to skimp on the job and stint on materials
which is similar to that by Dict.cn. This is likely a more precise translation, but less succinct.
3. Possible differences?
The 偷工 in 偷工减料 refers to "skimping on the job" (Yabla), so it should be business related. In English, we might say e.g. after a long day, our mother cuts corners when cooking dinner to emphasize that she makes a quick-and-simple meal, where it would be inappropriate to use 偷工 or 偷工减料: she is not a worker. (Perhaps better is 抄近路 = "to take a shortcut".)
The 偷 in 偷工 indicates a somewhat clandestine nature (as in 偷偷 = "secretly"). Perhaps a kind of trickery. However, cutting corners is not necessarily secretive.
The phrase 减料 (literally "reduce materials") within 偷工减料 itself conjures up using less materials in order to reduce costs. This doesn't match well with "cutting corners" in English, but would be better described as "skimping" or "stinting".
4. Intentionally purchasing an inferior product?
Can I use 偷工减料 to describe intentionally purchasing [an] inferior product that everyone knows about?
This doesn't seem to be a good match. My impression is that 偷工减料 is about shortchanging someone in terms of work or materials. To illustrate, other examples of 偷工减料 are:
Why [are] [Mercedes] Benz and BMW discounts increasingly ruthless? Are factories cutting corners?
We share [with] everyone a few kinds of obviously cut-cornered ice-creams...
Soviets in pursuing output, didn't hesitate to cut corners, even if it is a sub-standard product [they were] used in numbers.
Note: Despite the other answers claiming otherwise, I cannot conceive of nor did I find in a dictionary (1, 2, 3, 4) a neutral or positive interpretation of "cut corners". Indeed, the purpose of saying "cut corners" is to emphasize how a non-cutting-corners method or product is superior. (This is similar to Bathrobe's comment.)