The woman aged in her 50s was targeted in the graveyard on Staincliffe Hall Road bewteen 4.20pm and 4.35pm on Monday.
The man tried to grab the handbag from her shoulder, but she resisted and the suspect fled empty handed.
The suspect is described as a white male, around 25-years-old, 5ft 10ins tall, of slim build, with light, brown hair and an unshaven face.
He was wearing a blue sweatshirt with a white checked shirt underneath.
Officers are appealing for anyone who witnessed the incident or anyone who saw a man fitting the description above to please get in contact with police.
Information can be passed to Kirklees CID on 101 by quoting crime reference 13170153083 or anonymously to Crimestoppers on 0800 555 111.