A nipper or tile nipper is a tool

Tool

A tool is a device that can be used to produce an item or achieve a task, but that is not consumed in the process. Informally the word is also used to describe a procedure or process with a specific purpose. Tools that are used in particular fields or activities may have different designations such...

 used to "nip" or remove small amounts of a hard material, such as pieces of a tile

Tile

A tile is a manufactured piece of hard-wearing material such as ceramic, stone, metal, or even glass. Tiles are generally used for covering roofs, floors, walls, showers, or other objects such as tabletops...

 which needs to be fitted around an odd or irregular shape

Shape

The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...

.

For tile that requires a straight cut a tile cutter is used. This is a small mechanical device where the tile is placed, aligned and clamped on a platform; lightly "scored" with a cutting wheel and snapped in two with a handled slicer (blade similar to a paper cutter in appearance).
For larger jobs an electric tile saw or wet saw is used; this saw is similar to a small mitre saw except that water is distributed on the saw blade to lessen the effects of heat and friction.

A rail nipper is used in rail transport modelling

Rail transport modelling

Railway modelling or model railroading is a hobby in which rail transport systems are modelled at a reduced scale...

 to cut rail tracks.