For the second month in a row, deposits declined at savings and loan institutions in October as savers withdrew nearly $1 billion more than they deposited, the government reported yesterday.

The Federal Home Loan Bank Board also said that new mortgage loans rose to near-record volumes last month.

In the first 10 months of 1985, deposits fell by $4.0 billion overall, compared with deposit growth of $47 billion during the same January-October period last year, the bank board said. In October alone, withdrawals topped deposits by $997 million, the bank board reported.

The decline in deposits -- although not as pronounced as the $5.1 billion decrease in September -- followed a general year-long trend of reduced savings. The September decrease was the largest of the year. Economists said it was related directly to the giant increase in auto sales that month as depositors dipped into their savings to help finance new car purchases.

The bank board said that mortgage loans closed during October totaled $18.4 billion, up from $17.6 billion in September. The total also was the second-highest amount on record, surpassed only by the $19.8 billion in mortgage closings during June 1984.