Organic material will always contain carbon. A pure inorganic material will not - this is a definition, but doesn't really help you analyse a material.
A simple test would be to burn your material, and collect the combustion gases (smoke) and bubble these through a solution of lime water.
Any carbon in your sample will react with oxygen in the air and convert to carbon dioxide (CO2). CO2 makes lime water look like milk, so this is an easy qualitative test for the presence of carbon in a material.
Lime water is calcium hydroxide [Ca(OH)2] dissolved in water. the calcium hydroxide reacts with CO2 to make calcium carbonate (chalk!) which is an insoluble white solid, this makes the solution look milky
You say that you want to separate organic and inorganic material - you need to provide a bit more detail about the materials you are working with as there are many different types of separation techniques available, each technique is appropriate for different combinations of material.
In general, in order to identification the compounds are organic you can use FT_IR which refereed to position of C=C , C-C,..... peaks at more than 100 cm-1 or by combustion under O2 and collected the lbrated gas in container filled by Ca(OH)2 solution, hence, the librated CO2 will react and formed CaCO3 as ppt. But, the inorganic compounds can be studied by XRD....
To distinguish between organic and inorganic material . On burning on oxidized Cu gauze organic leaves no residue while Inorganic material leaves residue. Inoganic compds. are insoluble in organic solvents while organic material s are soluble in organic solvents. M.P. of Organic compds. are lower but that of Inorganic compds. are very much higher.