I think Christian's may work if you set the DisplayAlerts parameter to $false. 
Try the below, replacing the path: 
$filePath = "path\to\excel.xslx" # replace filename
# function pulled from http://stackoverflow.com/questions/5544844/how-to-call-a-complex-com-method-from-powershell
# allows for calling complex COM object's methods... I can define which arguments I want to send in
Function Invoke-NamedParameter {
    [CmdletBinding(DefaultParameterSetName = "Named")]
    param(
        [Parameter(ParameterSetName = "Named", Position = 0, Mandatory = $true)]
        [Parameter(ParameterSetName = "Positional", Position = 0, Mandatory = $true)]
        [ValidateNotNull()]
        [System.Object]$Object
        ,
        [Parameter(ParameterSetName = "Named", Position = 1, Mandatory = $true)]
        [Parameter(ParameterSetName = "Positional", Position = 1, Mandatory = $true)]
        [ValidateNotNullOrEmpty()]
        [String]$Method
        ,
        [Parameter(ParameterSetName = "Named", Position = 2, Mandatory = $true)]
        [ValidateNotNull()]
        [Hashtable]$Parameter
        ,
        [Parameter(ParameterSetName = "Positional")]
        [Object[]]$Argument
    )
    end {  ## Just being explicit that this does not support pipelines
        if ($PSCmdlet.ParameterSetName -eq "Named") {
            ## Invoke method with parameter names
            ## Note: It is ok to use a hashtable here because the keys (parameter names) and values (args)
            ## will be output in the same order.  We don't need to worry about the order so long as
            ## all parameters have names
            $Object.GetType().InvokeMember($Method, [System.Reflection.BindingFlags]::InvokeMethod,
                $null,  ## Binder
                $Object,  ## Target
                ([Object[]]($Parameter.Values)),  ## Args
                $null,  ## Modifiers
                $null,  ## Culture
                ([String[]]($Parameter.Keys))  ## NamedParameters
            )
        } else {
            ## Invoke method without parameter names
            $Object.GetType().InvokeMember($Method, [System.Reflection.BindingFlags]::InvokeMethod,
                $null,  ## Binder
                $Object,  ## Target
                $Argument,  ## Args
                $null,  ## Modifiers
                $null,  ## Culture
                $null  ## NamedParameters
            )
        }
    }
}
# create Excel COM object, set to suppress alert boxes
$excelapp = new-object -com Excel.Application
$excelapp.displayalerts = $false
# open workbook with CorruptLoad = Repair
[void](invoke-namedparameter $excelapp.workbooks "Open" @{"Filename"=$filepath; "CorruptLoad"=2})
# save repaired file and close
$excelapp.activeworkbook.saveas($filepath)
$excelapp.quit()