Mudd, now aged 20, carried out 594 of the distributed denial of service (DDoS) attacks himself, against 181 IP addresses, between December 2013 and March 2015.
He has admitted security breaches against his own college while he was studying computer science.
The attacks on West Herts College brought down the network and cost about $3600 to investigate but caused "incalculable" damage to work and productivity, the Old Bailey heard.
Polnay said: "This was not a white hat, friendly test to see what was going on."
On one occasion in 2014, the college hacking affected 70 more schools and colleges, including Cambridge University and the universities of Essex and East Anglia as well as local councils.
Polnay said there were more than 112,000 registered users of Mudd's programme who hacked over 666,000 IP addresses. Of those, nearly 53,000 were in the UK.
Among the targets was the fantasy game RuneScape, which had 25,000 attacks.
It cost its owner company nearly $12 million to try to defend itself against DDoS attacks with a revenue loss of $335,000.
Other hacking targets included Minecraft, Xbox Live, and the computer gamers' communications tool TeamSpeak.
The court heard Mudd created Titanium Stresser in September 2013 using a fake name and address in Manchester.
Until September 2015, 16 different computer servers were used to host the TitaniumStresser.net site.
The source code for the programme was found in Mudd's computer and listed "the muddfamily" as its founder or owner in the administrator records.
Polnay added: "This is a young man who lived at home. This is not a lavish lifestyle case.
"The motivation around this we tend to agree is about status. The money-making is by the by."
When he was arrested in March 2015, Mudd was in his bedroom on his computer which he refused to unlock before his father intervened.
Mudd pleaded guilty to one count of doing unauthorised acts with intent to impair the operation of computers, one count of making, supplying or offering to supply an article for use in an offence contrary to the Computer Misuse Act, and one count of concealing criminal property.
Judge Michael Topolski QC said the case was of "importance and seriousness" and not to be rushed to judgment.
"What he was seeking to acquire was his position in his world - status," he added.
"I have a duty to the public who are worried about this, threatened by this, damaged by this all the time ... It's terrifying."
Mudd, who has Asperger's Syndrome, is due to be sentenced next week.