A surprise dividend cut by General Motors sent stock market investors running for cover yesterday, as the Dow Jones Industrial Average dropped 14.81 points to close barely over the 800 mark.

The drop comes on top of an 8.23 point decline on Monday and means that the market in two days has erased much of the rebound that took place last week in the initial euphoric response to President Carter's dollar defense measures.

Now, however, it seems that the market is beginning to worry about the possibility that the high interest rates that are the cornersone of the president's program will induce a recession and send corporate profits down. At least that was the message investors got from the G.M. cut in its 1978 divident to $2.50 from 1977's record $3.25. Last week, G.M. reported record sales and profits for the first three quarters of the year.

"It suggests that G.M.'s internal projections are much more negative than their external statements" about the outlook of auto sales, said Newton Zinder, a vice president with E. F. Hutton.

Michael Metz, a vice president with Oppenheimer Co., in the trading department, said "There was a lot of disappointment over the G.M. dividend, as much for what it forecasts about the future as it tells us about the past. It indicates the pattern for industry generally will be more conservative, to be a little reticent over the 1979 outlook, and to husband financial resources."

G.M., one of the market's biggest capitalized stocks and a key component of the Dow 30 industrials, had a delayed opening that put it down 2 1/4 points. It closed the day down 1 7/8 points to 58 1/2.

Last week the chairman of IBM, Frank Cary, forecast slower growth for his closely followed company's computer sales next year which also depressed the market.

The rest of the news also was largely negativel yesterday and shadowed stock trading. The worrisome situation in Iran raised fears about the possible impact on petroleum supplies and petroleum prices, with an OPEC meeting scheduled for December.

The dollar also showed renewed signs of weakness after several days of stability. And gold started going up in price again.

The stock market acutally recouped some of its lost ground near the close, after having been down more than 18 points earlier in the session.

But the market's retreat was extremely broad, as about 1,416 issues delcined with only some 200 stocks higher on the New York Stock Exchange.

Volume totaled only 25.4 million shares, up from Monday's total of 20.4 million, but a far cry from the 50-million-share days experienced last week.

The broader NYSE Composite Index was down 0.81 to 52.22.

Among Big Board most actives, Pan Am was down 1/8 to 7, Ford Motors dropped 3/8 to 39 7/8, and Eastmen Kodak was down 3/4 to 58 1/4. Bally Manufacturing bucked the downdraft and closed up 1 5/8 to 38 3/4.

Big drops were recorded by Du Pont, which declined 3 5/8 to 122 5/8, and by Superior Oil which retreated 10 1/2 to 274 1/2. Both companies said they knew of no reason for the declines.

The American Stock Exchange Index was down 2.90 at 141.58. Some 105 issues gained with about 570 lower.

And the NASDAQ Composite Index of over-the-counter stocks dropped 2.25 to close at 112.83.