Splicing/Dividing a shape down an axis

So I have an object that I wish to divide in two down an axis, and I can’t figure out how to do it.

I can mirror the entire object, but I wish to do a part and then mirror it. Is there a way for effective grouping or merging of shapes to keep it all together, and can I split shapes such as an Icosphere in two through an axis.

Sorry if this is asked a lot; just getting started here.

Example shot:

http://gyazo.com/2b4d34985f45843f5740a5ec835aaadd.png

I wish to split along the Y axis. Then after mirroring, I wish to group the two halves back into one shape.

I’m not sure i clearly understand, but in Edit Mode, select the half of your model you want to separate and move.
Press P then choose “Selection” when prompted, it will make the selection a separate object.

Go to Object Mode, select the separated part of the model and move it along the axis you want (press G then Y to move it along the Y axis)
http://i.imgur.com/zNrI0.jpg

To regroup both separate object as a single one, select both and press CTRL+J

I think the mirror modifier should be mentioned here.