You can manufacture your critter using either a 2D printer or a 3D printer.

2D printer

Visit this page and drop your critter PNG onto it to generate pages. Print the pages so that each layer is a different page on a color printer. Then use scissors and glue to assemble each layer!

3D printer

Visit this page and drop your critter PNG onto it to generate a 3D printable STL file.

The above shows three STL files loaded into MakerWare: unsmoothed, smoothed with surface nets and smoothed with marching cubes.

https://voxelbuilder.com/img/anigif.gif