As I have said before, read his February 2000 Congessional testimony.
He said:
1. Pay down the national debt.
2. If you (Congress) can not resist the temptation (in other words, no backbone) to dip into the surplus, do a moderate tax cut rather than increase spending.
In the same speech, he also criticized Congress for some of the small tax cuts and spending increases that they tried to implement in 1999.
As any Economics 101 student knows, when the economy is hot, government cutting taxes or increasing spending is stimulative and will likely lead to higher inflation. The Fed's number one goal, which was mandated by Congress, is to fight inflation.
Added:
Although he does not say so in the speech, he advocates tax cuts over additional spending in the hope that some of the stimulative impact will be blunted by some people choosing to save their extra cash rather than spend it. But that is only a hope. Most evidence suggests that people spend nearly all of a tax cut when it is not directly linked to an incentive or requirement to save (such as an IRA deduction).
Rather than relying on people twisting his words, here is a link to read all of Greenspan's words. Think for yourselves:
Fed Reserve Text