Illustrator provides the following methods to cut, divide, and trim objects:
Methods for cutting, dividing, and trimming objects
Divide Objects Below command
Acts as a cookie cutter or stencil, using a selected object to cut through other objects, discarding the original selection. To use this command, choose Object > Path > Divide Objects Below. See Cut objects using the Divide Objects Below command.
Cut Path At Selected Anchor Point button
Cuts a path at the anchor point, and the one anchor point becomes two anchor points with one located directly on top of the other. To access this button, select one or more anchor points with the Direct Selection tool and locate the button in the Control panel. See Split a path.
Cuts objects along a freehand path you draw with the tool, dividing objects into their component-filled faces (a face is an area undivided by a line segment). Click and hold the Eraser tool to see and choose the Knife tool. See Cut objects using the Knife tool.
Splits a path, graphics frame, or empty text frame at an anchor point or along a segment. Click and hold the Eraser tool to see and choose the Scissors tool. See Split a path.
Split Into Grid command
Lets you divide one or more objects into multiple rectangular objects arranged in rows and columns. You can precisely change the height, width, and gutter size between rows and columns, and quickly create guides for laying out artwork. To use this command, choose Object > Path > Split Into Grid. See Divide an object into a grid.
Compound paths and compound shapes
Provide various ways to divide and trim overlapping objects. See Pathfinder.
Let you use an object to hide portions of other objects. See Clipping masks.
Cut objects using the Divide Objects Below command
Cut objects using the Knife tool
Divide an object into a grid
To set the size of each row and column, enter values for Height and Width.
To set the amount of space that separates rows from one another and columns from one another, enter values for Gutter.
To change the dimensions of the entire grid of objects, enter values for Total.
To add guides along the row and column edges, select Add Guides.