The sixth of ten children and the second of four sons born to Caleb Whims and Rachel Kerr, Joshua and his siblings grew up near Hookstown, Pennsylvania. On April 18, 1861, less than a week after Confederates in Charleston, South Carolina opened fire on Fort Sumter, he enlisted as a private in Company D, 22nd Ohio Infantry (3 months) and served until August 19, during which time the regiment was involved in a few small skirmishes. When his term of service expired, he returned home to Beaver County.

On August 22, 1862, at the public square in front of the county courthouse, Joshua mustered as a private in Company H, 140th Pennsylvania Volunteer Infantry, along with his younger brothers Jasper and Newton. The regiment was deployed to Parkton, Maryland for several months of guard duty along the Northern Central Railroad, during which time Joshua was promoted to corporal. In December the regiment joined the Army of the Potomac's 1st Division, II Corps, near Falmouth, Virginia, just days after the Battle of Fredericksburg, while the wounded were still being evacuated by train to Aquia Landing. Joshua subsequently fought in the Battle of Chancellorsville and the Siege of Petersburg.* According to his niece Minnie, her father Newt "liked to tell of one experience in the war. After [his] first battle [most likely Chancellorsville], he noticed that his older brother Joshua was standing beside him, when he should have been in another place. (A very serious thing for a soldier to do.) Father asked him what he was doing there, and Uncle Joshua replied, 'I wanted to see how the little boy was taking it.' Father then asked, 'How did I?' 'Splendidly,' Uncle Josh replied, 'but your face was as white as snow.'"

On December 9, 1864, the 1st Division, II Corps, was sent south of Petersburg on a reconnaissance along Vaughan Road toward Armstrong's Mill, with the 140th Pennsylvania in front as skirmishers. The regiment encountered Confederate resistance, and Joshua was shot near Hatcher's Run. He had his left arm amputated by the regimental surgeon and spent the rest of the war convalescing in Union Army hospitals. He was finally discharged on May 20, 1865 in Chester, Pennsylvania.

Joshua settled in Pottawatomie County, Kansas in 1867 and was elected the county's register of deeds in November 1869, followed by five subsequent re-elections. He also served on the executive committee of the Ex Sailors' and Soldiers' Association of Pottawatomie County and was a charter member of Oklahoma Post No. 4 of the Grand Army of the Republic, as well as its quartermaster, and served as president of the Wamego, Kansas chapter of the National Christian Temperance Union. He and Martha "Mattie" McGuire were married in Westmoreland, Kansas on November 24, 1872 and had seven children (Newton Lewellyn, Jasper Levi, Laura Isabelle, Wilbert Chapman, Edward Kerr, Rachael Ethel, and Ada Marion), but they separated at some point after 1893 and Joshua spent his final years in Los Angeles and San Diego, at one time living with his brother Newt's family.

Joshua's funeral service was held in a parlor at the corner of Third and Ash streets, under the auspices of the U.S. Grant Circle, No. 26, Ladies of the G.A.R.

* From his muster rolls Joshua appears to have been hospitalized for illness during the battles of Gettysburg, the Wilderness, Spotsylvania, and Cold Harbor.