Wall Street firms are cleaning out their desks — institutional-equity desks, that is.

Large and midsize firms are giving the boot to hundreds of high-priced trading staff in widespread layoffs and deep cost-cutting, replacing flesh-and-blood staff with cold steel computers and high-frequency trading algorithms.

The wholesale bloodbath is not painful to Wall Street’s profits, which are reaching historic highs. (New York Stock Exchange member firms’ profits tripled last year, to $24 billion, up from $7.7 billion in 2011. And this year opened with an outsize financial flourish. )

“The first quarter of 2013 was the biggest profit quarter in the history of the American banking industry,” said analyst Dick Bove.

But with equity and other trading in the doldrums, Dodd-Frank regulations casting a dark shadow, and, notably, advanced trading technology eliminating manual intervention, the Street is swinging the ax.

Many traders are now seen as “expenses” as the Street faces an uncertain and volatile future.

“We’ve had to shut it down,” industry veteran James Ross told The Post, describing the recent decision to close an innovative electronic-trading system operated by the AX Trading Group in Stamford, Conn.

Ross, chief operating officer at AX, said market conditions, declining volume and difficulty in raising capital imperiled AX’s future. AX employed seven pros.

It’s all just part of a wider contraction. “I had a couple of trading spots open since January, and I must have received about 3,000 résumés,” said Kyle Ramkissoon, a recruiter at IJC Partners.

There have been other high-priced layoffs across the Street in the past few weeks. (The typical pink-slipped pro made $500,000 a year; the best-of-breed pulled down millions.)

* Glenview Capital, a $5.5 billion hedge fund in the GM Building, cut four of its trading pros and analysts since the beginning of the year despite excellent returns.

* Bank of America Merrill Lynch has canned about a dozen traders so far this year in multiple rounds of layoffs. “There are more empty desks than full desks on the trading floor,” a source said.

* Both Credit Suisse and UBS eliminated teams of sales traders. “Credit Suisse doesn’t have that many in New York, and it let four go. That’s a lot,” a source said.

“I had a conversation a week ago with a fund that was trying to save some trading jobs,” said Harold Bradley, former head of trading at American Century. “They are trying to reorganize.”

Bradley said “buy-side” institutional traders are now up against what their “sell-side” counterparts at brokerage houses and exchange floors have faced for years, and are fighting big-time today — a sharp contraction in jobs.

“The cutbacks would tend to depress compensation for traders,”said Jim Leman, a managing director and trading expert at Westwater Corp.