Recent undercover operations by the Agriculture Department have led to the arrest of 63 persons in Chicago and Indianapolis on charges of food stamp fraud, in another blow struck for President Reagan by USDA Inspector General John V. Graziano.

One of Reagan's major political themes has been the need to cut welfare costs by weeding out welfare cheaters. Graziano has pursued that goal so diligently that the House Agriculture subcommittee on Department Operations, Research and Foreign Agriculture recently questioned whether he was spending too much time sniffing out individual chislers at the expense of more significant auditing assignments.

Such critics will have a tough time complaining about USDA's Chicago probe, which resulted in 42 arrests, including 24 federal employes. Those arrested had illegally obtained more than $500,000 worth of food stamps, USDA said. The Indianapolis probe resulted in 21 arrests, mostly store owners, who were accused of buying $16,445 in food stamps at a discount from recipients.

A recent probe, however, raised eyebrows on Capitol Hill. It involved a 33-year-old Texas house painter who was arrested after an eight-month investigation and a nationwide search by USDA.

The agency claimed the man filed at least 75 applications for food stamps in 23 states during a two-year period and had pocketed $14,000 in stamps by telling welfare workers that he was unemployed and needed emergency food stamps to feed his four children.

Some members of Congress wondered if the size of the fraud justified the scope of the investigation. The agency said it would be impossible to determine how many man-hours and what expense went into nabbing the man.