Here are some ways :
1. You can use split raster tool (Data management)
ArcGIS Help 10.1
2. If you have boundaries to clip the data then you can use clip tool (Data Management) to clip the big raster in small part according to boundaries. e.g. if you have raster of a State and would like to divide in Counties then you can use the County boundaries to clip the State raster
ArcGIS Help 10.1
3. You can create fishnet tool to generate polygons. Then you can use the fishnet as clipping feature and clip the big raster.
ArcGIS Help 10.1
4. If you have a spatial analyst you can try using Extract by mask tool to divide big raster in small parts.
ArcGIS Help 10.1
Regards
Kishor