Secretary of Health and Human Services Patricia Roberts Harris boasted yesterday that her department has saved taxpayers $1.7 billion in 15 months, and strongly questioned whether Ronald Reagan could cut another $14 billion to $20 billion from HHS outlays if elected president.

Reagan, in a Sept. 9 statement, said he would like to cut government spending by 2 percent at first and by 7 to 10 percent within five years, largely by eliminating waste and fraud in government programs. He didn't spell out where the cuts would be made, but if the 7- to 10-percent rate were applied to all departments, it would mean a slash of $14 billion to $20 billion in HHS funds, bases on its current annual budget of $195 billion.

"I do not know how it could be done," Harris said after reporters pressed her to say whether Reagan could realistically cut HHS spending that much purely by cutting fraud and waste.

Harris added that when the GOP was last in power, from 1969 to 1976, "it was not done." Only after the Democrats returned to power in 1977 did the present concerted effort to slash fraud, waste and inefficiency begin, she said.

Harris' remarks came at a news conference called to announce that, through management improvements and elimination of waste and abuse, HHS had saved $1.7 billion in the 15 months ending last Jan. 1. These steps included improved auditing, attempts to uncover welfare ineligibles, more accurate processing of Medicaid claims and the like.

Harris said waste in the Supplemental Security Income welfare program had dropped from 6.9 percent in 1976 to 4.9 percent in 1979. She said the figure in the program of Aid to Families with Dependent Children dropped from 10.6 to 9.5 percent.

She said her goal for savings in fiscal 1981 is $2.1 billion.

For the first time publicly, Harris took issue with a report by the HHS inspector general in 1978 -- before she became secretary -- asserting that the department might be wasting up to $7.4 billion a year.

She did not dispute the figure, but said it had been widely misinterpreted as meaning that the total amount was attributable to fraud or questionable payments.

Actually, she said, the report made clear that only about $2.7 billion was waste that could be saved by departmental action. The rest, she said, merely detailed possible sayings if Congress rewrote the programs to eliminate features the department considered undesirable.