Police confirmed they are investigating a series of offensive messages directed at the ex-England striker, which were sparked after the pundit suggested Liverpool striker Luis Suarez cheated by diving during last Saturday's match against Aston Villa.
Collymore retweeted some of the abuse he has received since the match - three days ago - to his 503,000 followers as he called on Twitter to take action.
He wrote: "In the last 24 hours I've been threatened with murder several times, demeaned on my race, and many of these accounts are still active. Why?
"I accuse Twitter directly of not doing enough to combat racist/homophobic /sexist hate messages, all of which are illegal in the UK."
He added later: "Several Police forces have been fantastic. Twitter haven't. Dismayed."
Later the 42-year-old, whose clubs in the 1990s included Liverpool, Aston Villa and Nottingham Forest, said he was in contact with Staffordshire police about the abuse.
He tweeted: "Staffordshire Police coming, again. Just the 5th time. Pity twitter aren't interested.
"Police take all complaints seriously,whoever it is. I've waited 6 weeks for twitter to provide information to Police. Yet to respond."
Broadcaster Piers Morgan was also subjected to abusive tweets after he joined calls for police and Twitter to take action over the abusive messages aimed at Collymore.
The former tabloid editor tweeted: "I repeat, racist abuse & death threats both criminal offences in UK. So keep spewing it, trolls, and I will have you ALL dealt with."
West Midlands Police confirmed on its Twitter page that Staffordshire Police were investigating "alleged abusive tweets to Stan Collymore" and urged people to block and report abuse at www.report-it.org.uk.
A Twitter spokeswoman said the company was unable to comment on individual users.
However, she pointed out that targeted abuse was against its rules and the site had recently made it easier for users to report abusive messages to them.
There are "established processes" in place for working with law enforcement, the spokeswoman added.