AS HE GOES patrolling through the budget with his hatchet and pruning shears, David Stockman is naturally drawn toward the subsidies for synthetic fuels. They attract him as a large and tangled overgrowth might attract any gardner with an orderly mind. After the gasoline shortages of 1979, Congress and the Carter adiministraton collaborated anxiously in a profusion of competing and conflicting programs to speed up the production of synthetic fuels. Mr. Stockman, as the Reagan administration's chief budget-cutter, sees an opportunity here.

There's a strong case for government support of synthetic fuels technology if it's done the right way. The right way is through the new federal Synthetic Fuels Corporation. It is preparing to offer loan and price guarantees to limit the risk to companies that embark on large ventures, testing genuinely new ideas, on which they are prepared to bet substantial among of their own money.

The wrong way is let the Department of Energy try to choose which technologies to develop and then pay companies to study them. It's slower, it's more expensive and it tends to undercut the Synthetic Fuels Corporation. Under the last administration, the Department of Energy intended to subsidize five plants making oil and gas from coal. The Congressional Budget Office, in its current list of possible budget cuts, observes that this kind of development can safely be left to private business. The rise in oil and gas prices has made federal support for these plants far less important, yet the subsides seem to run on automatically. Canceling the support for these five plants would save the federal government $2.8 billion over the next five years.

Mr. Stockman might also want to run his eye down the list of projects that the Carter administration had selected last December for the next round of subsidies. There's strong hint of pork barrel. A lot of the money would go into process for making fuel alcohol from grain. These process aren't very new or exciting. Fuel alcohol is already heavily subsidized. The wisdom of diverting food stocks to motor fuel is certainly dubious. Here's another candidate for cutting.

The Mobil Research and Development Corporation is also on that list. It would like $25 million to help it study mine coal gasification, and Tenneco Coal Gasification Co. request $20 million to think about lignite.Would Mobil and Tenneco be less creative if they were spending only their own money? The Weyerhaeuser Company is asking for $4 million to help it find a method of using wood chips instead of gas and oil to heat boilers. Does Weyerhaeuser, an ingenious company, really need federal aid to develop technology to burn its wood chips? A dairy in New York state is applying for $121,000 to make methane from cheese whey.The Rocket Research Co. of Redmond, Wash., is in line for $369,000 to study the possibility of a plant in Idaho to make alcohol from potato waste.

Are you there. Mr. Stockman? Do you have your clippers?