Can bacteria be killed by purely physical trauma?

...cut with a knife...

Yes, freeze them.... slowly. <evil laugh>

Freezing causes ice crystals to form inside the cells. These act like little knives. The slower the freezing happens, the larger these ice crystals get. The larger the ice crystals, the more damage they will do by piercing the cell wall and other important membranes.

This is why if you freeze fruit in a home freezer it thaws out as a goopy mess; the cell walls have been punctured. This is also a key problem in cryogenics, the freezing and thawing process damages cells.

Flash freezing uses very rapid freezing to very low temperatures to prevent large ice crystals from forming and minimizing damage. Food which is flash frozen is less goopy.

Note that when done properly freezing can be used to reliably kill some microbes, freezing at home is not a reliable disinfectant.

My (limited) understanding is that it is quite hard to avoid killing some bacteria even with very gentle physical manipulation. On the other hand, it is quite hard to use physical force to achieve reasonable level of sterilization. Let's bring some examples with a few (hastily found) references.

Pressure

My guess is that most examples the OP mentions (hit with a hammer, knife) will exert their biggest effect on bacteria through a peak in pressure - bacteria are comparable in size to width of a moderately sharp knife edge and thus there will be more "crushing" than "cutting" even with a knife (Science of Sharp discusses that Chosera 1k - a very good stone - will sharpen a knife to 0.5 μm, Wiki has bacteria at 0.5 - 5 μm).

I recently collaborated on a project where initial interpretation of results was wrong simply because putting a glass slip over a sample to inspect it under a microscope caused around 10% of bacterial (B. subtilis) cells to die. Putting a small weight on the slip resulted in roughly 80kPa additional pressure applied and ~ 80% of the cells dying within 25 minutes. But 80% death rate won't do much to e.g. reduce risk of food poisoning - as long as there are nutrients, bacteria will regrow quickly.

As m4rio mentions in a comment to another answer, and in line with The effect of high pressure processing on the microbial, physical and chemical properties of Valencia and Navel orange juice you need to ramp up the pressure to 100s of MPa to achieve high efficacy. And even that may not work so cleanly - e.g., the linked paper mentions that after applying 600 MPa, bacteria regrew to detectable levels after 4 weeks of storage at 4°C. Killing all (or almost all) bacteria is just really hard.

Because it was fun, I'll also link to study showing that High pressure-processed guacamole (4 cycles, 689 MPa, 5 min each) is clean enough to not spoil for 30 days in 25°C.

Note: the two sources above were linked from a commercial vendor of high-pressure products and may thus be biased. While the exact numbers might be problematic, I think the main point is unlikely to be affected.

A review High-pressure processing – effects on microbial food safety and food quality mentions some limitations, e.g.:

Endospores tend to be extremely HPP resistant compared with vegetative cells, withstanding treatments of more than 1000 MPa

ascospores of heat-resistant moulds such as Byssochlamys, Neosartorya and Talaromyces are generally considered to be extremely HPP resistant

It should however be noted that it seems that high-pressure treatment is good enough to be semi-commonly used as the main sterilization for suitable foodstuffs - Current status and future trends of high-pressure processing in food industry reports high-pressure treatment to be FDA approved and USD 10 billion worth of food being treated as of 2015.

Pressure for killing cells previously briefly discussed at Can bacteria or other microorganisms be killed by applying pressure?

Ultrasound

While frequently used for cell lysis in lab, it also doesn't kill all cells. For example The Sterilization of Suspensions Contaminated with MicroorganismsUsing Ultrasound Irradiation reports that roughly 20-30% of bacteria (Bacillus) survived 60 minutes of ultrasound treatment.

Ball mill

This is probably closest to actual "physical trauma" - you put small beads and a suspension with microorganisms into a cylinder and roll it hard. A low energy process for the recovery of bioproducts from cyanobacteria using a ball mill discusses using this process to extract proteins from cyanobacteria. They don't report absolute number of cells killed, just that it varies considerably with the rotation speed, size of beads, .... My interpretation is that in most cases a non-negligible proportion of the cells survive while majority is killed (and their contents extracted for further use).

There are plenty of physical or mechanical methods of killing bacteria, but most are used in conjunction with other agents and probably don't qualify as "blunt force trauma". For example, beer distributers might snake a brush through a keg line to disrupt any bacterial biofilms before flushing them out with disinfectant. Similar logic applies to rubbing your hands together when you wash them or using a brush to scrub biofilms off your teeth. We might not think of it as traumatic force, but it can be to bacteria.

Since you mentioned it, there is something that might resemble them being "twisted until they burst" (more like crushed to death). A device called a French pressure cell press (or just French press) used to lyse bacterial cells with purely mechanical forces. It basically compacts a culture of cells under high pressure, causing them the burst and release the cellular contents. Of course, it would require somehow gathering all of them together into a containment vessel and having an expensive laboratory instrument to put them in.

From a biochemical point of view, it is surprisingly difficult to break open a bacterial cell. A molecular biologist, for example, might want to break E.coli cells expressing a protein of interest, in order to purify the protien

Some of the methods employed are agitation with glass beads, griding with glass beads, sonication, and high-pressure cell disruption with the French Press.

In contrast, liver cells, or brain cells, may be broken by simple homogenization (for example in a Waring blender)

Yes of course. While you can't swing a blunt object comparable in size to humans at something many orders of magnitude smaller to kill it. You can use something like an ultra sonicator, which swings a small blunt object at --you guessed it-- very high speeds to generate lots of shear forces in a liquid culture. Usually these instruments are not meant for killing cells, but even with my most gentle use for breaking up cell clumps, a look under the microscope would show ruptured cells with their interior spilled out.