You don't need to clone the repo to get the log. TeamCity already has a list of files and commit messages that triggered the build. You can simply query the TeamCity API in a script step and get the log. Here are the two Powershell functions I use to do this.
TeamCityGetChangeLog, requires the server url, the username, password, and a build ID (which you can pass in from the TeamCity parameters).
# Gets the change log for the specified build ID
function TeamCityGetChangeLog([string] $serverUrl, [string] $username, [string] $password, [int] $buildId){
    $changelog = ''
    # If the build is running inside TeamCity
    if ($env:TEAMCITY_VERSION) {
        $buildUrl = "$serverUrl/httpAuth/app/rest/changes?build=id:$($buildId)"
        $authToken = [Convert]::ToBase64String([Text.Encoding]::ASCII.GetBytes($username + ":" + $password))
        # Get all the changes
        $request = [System.Net.WebRequest]::Create($buildUrl)
        $request.Headers.Add("Authorization", "Basic $authToken");
        $xml = [xml](new-object System.IO.StreamReader $request.GetResponse().GetResponseStream()).ReadToEnd()
        # Get all commit messages for each of them
        $changelog = Microsoft.PowerShell.Utility\Select-Xml $xml -XPath `
            "/changes/change" | Foreach {
                TeamCityGetCommitMessage $serverUrl $username $password $_.Node.id
            }
    }
    return $changelog
}
That relies on TeamCityGetCommitMessage which also requires the change set ID.
# Get the commit messages, and files changed for the specified change id
# Ignores empty lines, lines containing "#ignore", "merge branch"" or "TeamCity"
function TeamCityGetCommitMessage([string]$serverUrl, [string]$username, [string]$password, [int]$changeId)
{
    $getFilesChanged = $false;
    $request = [System.Net.WebRequest]::Create("$serverUrl/httpAuth/app/rest/changes/id:$changeId")
    $authToken = [Convert]::ToBase64String([Text.Encoding]::ASCII.GetBytes($username + ":" + $password))
    $request.Headers.Add("Authorization", "Basic $authToken");
    $xml = [xml](new-object System.IO.StreamReader $request.GetResponse().GetResponseStream()).ReadToEnd()
    Microsoft.PowerShell.Utility\Select-Xml $xml -XPath "/change" |
        where { ($_.Node["comment"].InnerText.Length -ne 0) `
        -and (-Not $_.Node["comment"].InnerText.Contains('#ignore')) `
        -and (-Not $_.Node["comment"].InnerText.StartsWith("Merge branch")) `
        -and (-Not $_.Node["comment"].InnerText.StartsWith("TeamCity change"))} |
        foreach {
            $getFilesChanged = $true
            $username = (&{If($_.Node["user"] -ne $null) {$_.Node["user"].name.Trim()} Else { $_.Node.Attributes["username"].Value }})
            "<br /><strong>$($username + " on " + ([System.DateTime]::ParseExact($_.Node.Attributes["date"].Value, "yyyyMMddTHHmmsszzzz", [System.Globalization.CultureInfo]::InvariantCulture)))</strong><br /><br />"
            "$($_.Node["comment"].InnerText.Trim().Replace("`n", "`n<br />"))"
        }
    if ($getFilesChanged) {
        "<br /><br /><strong>Files Changed</strong><br /><br />"
        Microsoft.PowerShell.Utility\Select-Xml $xml -XPath "/change/files" |
        where { ($_.Node["file"].Length -ne 0)} |
        foreach { Select-Xml $_.Node -XPath 'file' |
            foreach { "$($_.Node.Attributes["file"].Value)<br />" }
        }
    }
}