For the purposes of this question I'm going to assume the monomolecular blade is about 1-2 water molecules across. Much smaller than that and quantum forces start to dominate and I'm not a quantum physicist, I'm a biologist.

Anyway. Such a blade behaves very strangely, and how much damage it does depends a lot on the kinetics of what you're doing with the target. A leg holding a person up, for instance, will be nearly completely unaffected. It might hurt, but not much and not for long. Cell membranes are, on the microscale, self-healing. They're built of phospholipids that self-assemble into two-sided layers, and if disrupted they reassemble very quickly.

Nerves are essentially long tubes made of cell membrane, and the opening in the membrane created by the blade's passage is not wide enough or long-lasting enough to damage the neuron.

The membranes will therefore mostly be fine, and any damage is small enough to be repaired by the body.

DNA deserves a quick look, but essentially any nucleus that the blade passes through will have its DNA shredded into hundreds or thousands of pieces, and even organisms capable of reassembling double-stranded breaks are bound to get it wrong at least once. Catastrophic DNA damage, and cell death follows. However, the slice of cells this actually happens to is pretty small, and cell death from DNA damage takes a few minutes minimum, so this isn't fatal or even particularly wounding.

Proteins are a different question entirely. Muscles are essentially extremely long proteins overlapping in a staggered configuration, and are nearly always under some amount of tension. The blade would cut these protein assemblages and they'd recoil, leaving a gap between muscle proteins. Laminins and the proteins that give structural strength to skin and connective tissue would also be cut neatly.

In terms of the bigger picture, the two bits of flesh would be structurally very weakly connected for the first . Two perfectly smooth surfaces stuck together with a sticky semifluid adhere fairly tightly, so even though the proteins are cut there's still some strength to the join. In a short period of time(seconds? less? The kinetics are complicated) the protein matrices that give strength to the tissue will recombine. Shortly after that blood clotting factors released by ruptured cells will glue together other damaged pieces of tissue. Note: the cells won't be ruptured by the blade, but more likely by the spring-loaded protein networks inside them suddenly moving.

Recovery of full strength may take days in the case of cartilage but there are few structures in the human body that aren't under constant remodeling.

If the body part is under strong forces at the time of the cut the two halves would peel apart before they can be knit back together, but the strength required is a question of strike speed, temperature, body viscosity, and some other unknowns.

NB: 'strong forces' are experienced by the heart every time it beats, so whether you live or die may be a question of whether your heart was beating when you got slashed with the monofilament or not.

For the purposes of this question I'm going to assume the monomolecular blade is about 1-2 water molecules across. Much smaller than that and quantum forces start to dominate and I'm not a quantum physicist, I'm a biologist.

Anyway. Such a blade behaves very strangely, and how much damage it does depends a lot on the kinetics of what you're doing with the target. A leg holding a person up, for instance, will be nearly completely unaffected. It might hurt, but not much and not for long. Cell membranes are, on the microscale, self-healing. They're built of phospholipids that self-assemble into two-sided layers, and if disrupted they reassemble very quickly.

Nerves are essentially long tubes made of cell membrane, and the opening in the membrane created by the blade's passage is not wide enough or long-lasting enough to damage the neuron.

The membranes will therefore mostly be fine, and any damage is small enough to be repaired by the body.

DNA deserves a quick look, but essentially any nucleus that the blade passes through will have its DNA shredded into hundreds or thousands of pieces, and even organisms capable of reassembling double-stranded breaks are bound to get it wrong at least once. Catastrophic DNA damage, and cell death follows. However, the slice of cells this actually happens to is pretty small, and cell death from DNA damage takes a few minutes minimum, so this isn't fatal or even particularly wounding.

Bones are a bit weird, but on that scale ossified cartilage(bone) is more like a sponge than a continuous material. See here for pictures. The space between the pores is filled with cartilage and other goopy things, but if the bone is under compression the spiky bits of sponge will jam into the holes on the other side and hold together enough to heal properly. If the bone was under tension it depends on the forces involved.

Proteins are a different question entirely. Muscles are essentially extremely long proteins overlapping in a staggered configuration, and are nearly always under some amount of tension. The blade would cut these protein assemblages and they'd recoil, leaving a gap between muscle proteins. Laminins and the proteins that give structural strength to skin and connective tissue would also be cut neatly.

In terms of the bigger picture, the two bits of flesh would be structurally very weakly connected for the first . Two perfectly smooth surfaces stuck together with a sticky semifluid adhere fairly tightly, so even though the proteins are cut there's still some strength to the join. In a short period of time(seconds? less? The kinetics are complicated) the protein matrices that give strength to the tissue will recombine. Shortly after that blood clotting factors released by ruptured cells will glue together other damaged pieces of tissue. Note: the cells won't be ruptured by the blade, but more likely by the spring-loaded protein networks inside them suddenly moving.

Recovery of full strength may take days in the case of cartilage but there are few structures in the human body that aren't under constant remodeling.

If the body part is under strong forces at the time of the cut the two halves might peel apart before they can be knit back together, but the strength required is a question of strike speed, temperature, body viscosity, and some other unknowns.

NB: 'strong forces' are experienced by the heart every time it beats, so whether you live or die may be a question of whether your heart was beating when you got slashed with the monofilament or not.