Stephen Lee Short made and shared five videos on social media of a woman putting a small dog into "various kitchen appliances".
In one of the clips, Short said the dog would be placed in the microwave and made anti-Semitic comments referring to the Holocaust, Wolverhampton magistrates heard.
Short, 32, of Capstone Avenue, Oxley, pleaded guilty to sending an offensive message by public communication at Wolverhampton Magistrates Court in May and was given a 12-month community order which included 15 rehabilitation activity requirement days, an alcohol treatment requirement and a 21-day thinking skills programme.
He was also ordered to perform 200 hours of unpaid work, which had been increased by 50 hours to reflect the racial element of the offence.
Details of the case have now been revealed by the Crown Prosecution Service.