A kaligraphon (a metal utensil comprised of a long shaft with prongs, or "teeth", at one end, which were used to take food out of the oven, and a flat scoop at the other end which was used to scoop out coal and ash)

whose scoop was removed

is tamei

because of its teeth (which leave the utensil with some utility),

if the teeth were removed,

it is tamei because of the scoop.

An eye-makeup applicator (another tool with a separate implement at each end)

whose scoop was removed

is tamei because of the pointed applicator at the other end

if the pointed applicator was removed

it is tamei because of the scoop (even though the scoop, which was used either clean out the ear or, others say, to remove makeup, was of lesser importance).

A stylus (used for writing in wax, this tool had a pointed nib on one end and was flat on the other end, for use as an eraser)

whose nib was removed

is tamei because of the eraser,

if the eraser was removed

it is tamei because of the nib.

A zomalystera (one end had a scoop for skimming froth from a pot or serving soup, the other tines for removing meat from the pot; others say this tool was used for roasting meat, with one end akin to a spatula, the other a three-pronged fork)

whose scoop was removed

is tamei because of the fork,

if the fork was removed

it is tamei because of the scoop.

And similarly the teeth of a mattock (an tool with a head that serves two roles, one side of the head has an axe-like blade, and the other side is shaped like an adze, which is akin to an axe-blade rotated 90 degrees; other interpret this as another agricultural implement like pitchfork or soil-tiller, with teeth on one end and a tool for joining plowing equipment at the other).

The measure for all of them (as too how much of the shaft must remain for it to still be tamei):

sufficient to do their job.

פרק יג משנה ג

A blade (this refers to the blade of a device similar to a hoe, made to cut roots or dig soil while plowing; it was composed of a cutting edge of high quality metal, and a body of lower quality )

that was damaged

is tamei until the majority of it (the cutting edge or body) is removed;

if its socket (where it was attached to the shaft that it was held by) was broken it is tahor.

an axe (with two blades on the head, one for cutting trees, the other for splitting logs) whose cutting blade was removed

is tamei because of its splitting blade,

if its splitting blade was removed

it is tamei because of its cutting blade,

it its socket (by which it was attached to the axe-handle) was broken it is tahor.