Group leader Colin Galloway said the city was no longer welcoming to businesses or tourists "because it seems we prefer to have vagrants".
He said he has seen "no action" while on a homelessness committee and wants police to forcibly put people in care.
Hampshire's Police commissioner called the comments "disgusting".
Police and Crime Commissioner Michael Lane described the language used as "appalling and offensive".
He added: "I am clear that the challenges of people living with vulnerabilities need to be dealt with in partnerships... it is a complex issue."
Matt Downie, director of policy at homelessness charity Crisis, said: "Referring to people as 'unwelcome detritus' is offensive in any circumstances, but it is all the more toxic when those people are homeless or struggling in desperate circumstances.
"Whether homeless or not, people who beg are often some of the most vulnerable in society and they deserve better than to be treated as a nuisance."
Portsmouth City Council estimates its number of rough sleepers has risen from 37 last autumn to 60 in May.
In a motion due to be debated at the full council meeting next week, Mr Galloway said there was "a lot of good intentions but virtually no action" on the homelessness committee.
"Portsmouth City is no longer a welcoming city to either business or tourist because it seems we prefer to have vagrants," he added.
"These beggars, vagrants, rough sleepers, homeless, troubled folks or whatever label you want to put on them must be removed from our city and placed in specific care whether they want to or not."
He called on police to "help us clean up this unwelcome detritus".
At the Portsmouth City Council meeting on Tuesday, Mr Galloway is set to urge council leader Donna Jones to write to Mr Lane to instruct police to "help the council to remove the ever increasing beggars and rough sleepers that are beginning to dominate the city".
Mr Galloway has been approached for comment.
4,134
rough sleepers a night in 2016
3,569
the year before
509 female
288 under 25
714 from other EU countries
194 from outside EU
A UKIP councillor has labelled homeless people "unwelcome detritus" and called for them to be removed from the streets of Portsmouth.