In IGI, the following children have Robert Mitchell and Rachel Johnston as their parents.
International Genealogical Index / British Isles - 6
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1. MARY MITCHEL - International Genealogical Index
Gender: Female Birth: 03 JUN 1859 New Monkland, Lanark, Scotland
2. MARGARET MITCHELL - International Genealogical Index
Gender: Female Birth: 24 MAY 1865 New Monkland, Lanark, Scotland
3. WILLIAM MITCHELL - International Genealogical Index
Gender: Male Birth: 15 APR 1857 New Monkland, Lanark, Scotland
4. WILLIAM MITCHELL - International Genealogical Index
Gender: Male Birth: 30 MAY 1861 New Monkland, Lanark, Scotland
5. SARAH MITCHELL - International Genealogical Index
Gender: Female Birth: 04 FEB 1863 New Monkland, Lanark, Scotland
6. SARAH MITCHELL - International Genealogical Index
Gender: Female Birth: 31 MAY 1855 Old Monkland, Lanark, Scotland
Also in IGI the is a marriage for a Robert Mitchell and Rachel Johnstons
14th jan 1846, Registrar Office, Ballymonet, Co. Antrim, Ireland
1861 census index for Bothwell, Lanarkshire
Robert Mitchell age 35 born Ireland
Rachel age 32 born Ireland
Robert age 14 born Ireland
Mary age 1 born Airdrie
1881 census shows Rachel as a widow
Dwelling: No 1 Row
Census Place: Bothwell, Lanark, Scotland
Source: FHL Film 0203617 GRO Ref Volume 625-2 EnumDist 15 Page 7
Marr Age Sex Birthplace
Rachel MITCHELL W 49 F Ireland
Rel: Head
William MITCHELL U 19 M New Monkland, Lanark, Scotland
Rel: Son
Occ: Coal Miner
Margaret MITCHELL U 15 F New Monkland, Lanark, Scotland
Rel: Daur
Hugh REILLY U 26 M Ireland
Rel: Boarder
Occ: Labourer At Iron Works
1881 census, think this could be Sarah
Dwelling: Victoria Place
Census Place: New Monkland, Lanark, Scotland
Source: FHL Film 0203697 GRO Ref Volume 651-2 EnumDist 11 Page 24
Marr Age Sex Birthplace
Robert ADAM M 54 M Airdrie, Lanark, Scotland
Rel: Head
Occ: Retired Draper
Agnes ADAM M 54 F Airdrie, Lanark, Scotland
Rel: Wife
James ADAM U 25 M Airdrie, Lanark, Scotland
Rel: Son
Occ: Draper
William ADAM U 23 M Airdrie, Lanark, Scotland
Rel: Son
Occ: Draper
Thomas ADAM U 20 M Airdrie, Lanark, Scotland
Rel: Son
Occ: Bank Clerk
Maggie ADAM U 17 F Airdrie, Lanark, Scotland
Rel: Daur
Charles ADAM U 15 M Airdrie, Lanark, Scotland
Rel: Son
Occ: Scholar
Agnes ADAM U 10 F Rothesay, Bute, Scotland
Rel: Daur
Occ: Scholar
Sarah MITCHELL U 18 F Airdrie, Lanark, Scotland
Rel: Servant
Occ: General Domestic
If this is your Mitchell family, then Robert Mitchell must have died between the years of 1865/6 (as daughter Margaret was born about then) and 1881 (before census)
Searching for Robert's death cert. will give you his parent's names, provided they were known by the informant.