Miss Alice, I can't find any "Mord Miller" in Booth's Record of Louisiana Confederate Soldiers or any record of him in Confederate service in the National Park Service's Civil War Soldiers & Sailors Systeem. That obviously doesn't mean his headstone is wrong. It just means he may be listed some other way. Here are the "Miller, M" listings from Booth's Records for you to look over...
Miller, M., Pvt. Co. A, Gordon's Mo. Cav. Roll of Prisoners of War, C. S. A., Paroled
Shreveport, La., June 7, 1865. Res. Carroll Co., Mo.
Miller, M., Pvt. Co. A, 2nd La. Cav. Roll of Prisoners of War, C. S. A., Paroled
Washington, La., June 16, 1865. Res. St. Landry Par., La.
Miller, M., Pvt. 10th La. Co. G. Federal Rolls Prisoners of War, Captured Gettysburg, Pa., _.
Transfd. to Pro. Mar., July 15, 1863, from U. S. Gen. IIospl., Gettysburg, Pa.
Miller, M., Pvt. Co. A, 14th La. Inf. En. July 27, 1861, New Orleans, La. Present on all Rolls
to Feb., 1864, Brigade teamster.
Miller, M., Pvt. Co. B, Cres. Regt. La. Inf. Roll May and June, 1862 (only Roll on which borne),
En. New Orleans, La., March 5, 1862. Absent, detached Gen. Beal's Comdg. Dept.
Miller, M., Pvt. Fowler's Co. Bragg's Battn. La. Mil. On Report dated New Orleans, La., Nov. 25,
Miller, M., __, Co. -, 2nd Regt. 2nd Brig. 1st Div. La. Mil. Appears on List not dated of the
Miller, M., Pvt. Co. 7, 4th Regt. French Brig. La. Mil. Appears on Roll not dated, ordered into
the service of the State of Louisiana.
Miller, M. A., Pvt. Co. B, 4th Regt. Engr. Troops. Roll of Prisoners of War, C. S. A., Paroled
Shreveport, La., June 7, 1865. Res. Cumberland, Tenn.
Miller, M. F., Pvt. Co. H, 28th (Gray's) La. Inf. En. Arcadia, Feb. 23, 1863. Roll July and
Aug., 1863, Present. On Hospl. Register, C., S. A., Gen. Hospl., Shreveport, La. Admitted July
15, 1864, Dropsy. Transfd. July 20, 1864, to Keachi.
Miller, M. M., Pvt. Co. D, Confed. Grds. Regt. La. Mil. Roll for March 8 to April 30, 1862 (only
Roll on file), En. New Orleans, La., March 8, 1862. Present. Note: Transfd. by T. O. Moore, Gov.
of the State of La., to Maj. Gen. M. Lovell, C. S. A., for local defense of the city of New
Orleans, La., March 8, 1862.
Miller, M. W., 1st Sergt. Co. D, 1st La. Arty. Roll of Prisoners of War, C. S. A., Paroled
Meridian, Miss., May 14, 1865. Res. Fort Adams, Wilkinson Co., Miss.
Miller, M. W., Ord. Sergt. 1st Sergt. Co. B, 8th Battn. La. Hvy. Arty. En. _. Federal Rolls of
Prisoners of War, Captured and paroled Vicksburg, Miss., July 4, 1863. On List dated Enterprise,
Miss., Oct. 13, 1863, Present, in parole camp. On List dated Dec. 11, 1863, without remark.