SharePoint Portal Server brings along document filters mostly for office documents. But you can also save and full text search your mindmaps in SharePoint.
If you are using Mindmanager X5 or the current version 6 then you are lucky and just have to look at ifiltershop.com. They've got a solution for indexing Mindmanager documents.
Sadly for Mindmanager 2002 there is no such IFilter available. But you can easily write your own! Mindmanager has an OLE automation interface where you can traverse the mindmap tree structure and extract all label texts from it. Then you have to tell the indexing service the texts. For that purpose Microsoft has defined the IFilter-COM-Interface, which you have to implement. The coding is pretty straight forward:
#import "MindMan.tlb"

// Init-Call from index service
HRESULT IFilter::Init(ULONG grfFlags, ULONG cAttributes, const FULLPROPSPEC* aAttributes, ULONG* pFlags)
{
    ImjApplicationPtr pMindManager(__uuidof(Application));
    pMindManager->Visible = VARIANT_FALSE; // hide GUI
   
    ImjDocumentPtr pMindManagerDoc = pMindManager->Documents->Add(_bstr_t("Mindmap.mmp")); // open mindmap
   
    do
    {
        // remember texts for every ImjBranchPtr pBranch
        PushText(pBranch->Text);
        PushText(pBranch->TextNotes);
    } while(...);
   
    pMindManager->Close(VARIANT_FALSE);
    ...
}

// index service calls this method and GetChunk() for every text until FILTER_S_LAST_TEXT is returned
HRESULT IFilter::GetText(ULONG* pcwcBuffer, WCHAR* awcBuffer)
{
    WCHAR* pwcNextText = PopText(); // get next text for indexer from memory
    if(pwcNextText != NULL)
    {
       *pcwcBuffer = wcslen(pwcNextText);
       wcsncpy(awcBuffer, pwcNextText, *pcwcBuffer);
    }
        return FILTER_S_LAST_TEXT; // no more texts available
}

There is only one problem with this approach - you have to install the Mindmanager product on your indexing server. Argh, this brings in most of the problems you have, if you run any Office product on a server. But the guys at Mindjet promised me, that it's ok and until now no strange effects happend on the server where i run it (as opposed to a braindead instable excel server i was replacing last year). So maybe your admins won't rip your heart out ;)